Find the eigenvalues and eigenvectors for the standard matrix : { 1 -2 0} {-2 -1 1} {0 0 -1}

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  1. Math

    Given the following matrix A, find an invertible matrix U so that UA is equal to the reduced row-echelon form of A: You can resize a matrix (when appropriate) by clicking and dragging the bottom-right corner of the matrix. A = 3 3 9 −6 3 3 9 −6 −2

  2. Algebra

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  3. algebra

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  5. Algebra

    2. Use an augmented matrix to solve the system. x + y = 5 3x – y = –1 (1 point) (1, 4) (1, 5) (3, –1)*** (5, –1) 3. When converting a system of linear equations into an augmented matrix, what equation form is needed? (1 point) slope-intercept form

  6. math

    verify The set of all 2 × 2 invertible matrices with the standard matrix addition and scalar multiplication is a vector space or not?

  7. Math

    Directions: Use the following matrix to perform the elementary row operations sequentially. A=[3 2 |8] [5 2 |12] 1.) (1/3) R1 From the original matrix 2.) -5R1+R R2 From matrix in question 1.

  8. Linear Algebra

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  9. Linear Algebra

    Consider the following system of linear equations: 2x1+2x2+4x3 = −12 x1+6x2−8x3 = −6 x1−2x2+9x3 = −8 Let A be the coefficient matrix and X the solution matrix to the system. Solve the system by first computing A−1 and then using it to find X. I

  10. Calc

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  11. Linear Algebra

    Given the following matrices A and B, find an invertible matrix U such that UA = B: A and B are 4x4 matrix and i have to find U. I was wondering how i would do this ie. the steps. if you could be as detailed as possible that would help me. I wanted to try

  12. Augmented Matrix

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  13. linear algebra

    which of the following sets of vectors span R^3? a.){(1, -1, 2), (0, 1, 1)} b.) {1, 2, -1), (6, ,3, 0), (4, -1, 2), (2, -5, 4)} c.) {(2, 2, 3), (-1, -2, 1), (0, 1, 0)} d.) {(1, 0, 0), (0, 1, 0), (0, 0, 1), (1, 1, 1)} can someone show the steps to check for

  14. math

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  15. linear algebra

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  16. Eigenvalues

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  17. Linear Algebra

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  18. Math

    Mark each of the following True or False. ___ a. All vectors in an orthogonal basis have length 1. ___ b. A square matrix is orthogonal if its column vectors are orthogonal. ___ c. If A^T is orthogonal, then A is orthogonal. ___ d. If A is an n*n symmetric

  19. Econometrics

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  20. maths

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  21. phys

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  22. linear algebra

    Use a calculator to find the inverse of the orthogonal matrix matrix Q=[ 0 0 1 −1 0 0 0 −1 0 ] and verify Property 1 above.

  23. math

    Diagonalize the given matrix and find an orthogonal matrix P such that P−1AP is diagonal -2 3 3 3 -2 3 3 3 -2

  24. Math: Linear Algebra

    Let T1: P1 -> P2 be the linear transformation defined by: T1(c0 + c1*x) = 2c0 - 3c1*x Using the standard bases, B = {1, x} and B' = {1, x, x^2}, what is the transformation matrix [T1]B',B T(c0 + c1*x) = 2c0 - 3c1*x ---> T(1) = 2 T(x) = -3x So, the matrix

  25. Math

    Let T: R^3 -> R^3 be a linear transformation whose matrix, with respect to the standard basis is |1 1 2| |1 3 0| |1 0 1|. If T^(-1){ |96| |u| | 2| = |v| | 3| |w|} then the value of v is?

  26. Linear Algebra

    (a) Show that if A is an m x n matrix and A(BA) is defined, then B is an n x m matrix. (b) Show that if A has a row of zeros and B is any matrix for which AB is defined, then AB also has a row of zeros. (c) Find a similar result involving a column of

  27. math

    When solving a system using elimination on a TI-84 calculator how do you do it? I forgrt all the steps heres the ones i know 1. 2nd (button) Matrix 2. Edit Matrix A 3. Edit Matrix B 4. 2nd (button) Quit what's next? Thanks

  28. math

    I need help with this one... Thanks!!!! Prove the following statement: When you add the identity matrix to a nilpotent matrix it is invertible.

  29. Linear Alebra

    Find the eigenvalues and eigenvectors for the standard matrix : { 1 -2 0} {-2 -1 1} {0 0 -1}

  30. Linear Algebra

    Find the eigenvalues and corresponding eigenvectors of the matrix: 0 0 1 M = 1 0 0 0 1 0

  31. eigenvalues/eigenvectors

    For the standard matrix { 1 -2 0} {-2 -1 1} {0 0 1} I found the eigenvalues to be -1, and +/- 5^1/2 I am having problems finding the eigenvectors of the root 5 values. Can someone set me straight?? Thanks

  32. linear algebra

    Find all eigenvalues and eigenvectors of matrix A=⎡⎣⎢11−2002−101⎤⎦⎥

  33. Math

    Went ahead and did the HW the teach recommended but she did not post the answers and I would like to see if im on the right track. Problem 1: Are the vectors (2,−1,−3), (3, 0,−2), (1, 1,−4) linearly independent? Problem 2 : Is the set {x E R^4 :

  34. masterin quantum

    Consider the left shift operator on the space of infinite sequences of complex numbers: L(z1,z2,…)=(z2,z3,…). Is L injective? Yes Yes - incorrect No Is L surjective? Yes Yes - correct No Find the eigenvalues and eigenvectors of L. Then complete the

  35. Linear Algebra

    For the matrix A below, find a value of k so that A has two basic eigenvectors associated with the eigenvalue λ = 3. A = [−3 −18 54 204 0 3 −18 −54 0 0 −3 k 0 0 0 3] k = ? I'm specifically having troubles reducing this and knowing what it'll

  36. eigenvalues/eigenvectors

    The matrix; [ 1 -2 0] [-2 -1 1] [ 0 0 -1] I have found the eigenvalues to be -1 and +/- 5^1/2 but am having problems putting the root 5 values a eigenvectors. I know I sub it back into the matrix { x-1 -2 0 } { -2 x+1 1 } { 0 0 x+1} but then it gets messy.

  37. math

    I am trying to find the eigenvalues . They are 0 and 2 but i keep on just getting 0. its a4X4 matrix. [ 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0]

  38. math

    Prove that if A is a symmetric n x n matrix, then A has a set of n orthonormal eigenvectors. http://ltcconline.net/greenl/courses/203/MatrixOnVectors/symmetricMatrices.htm I've read the entire page and while it's on the correct topic, it doesn't prove what

  39. Algebra

    for the matrix: { 1 -2 0} {-2 -1 1} { 0 0 -1} I found the eigenvalue to be -1 and +/- 5^1/2 Is this correct and can someone show me how to put the root 5 values as eigenvectors? Please and Thanks

  40. math,algebra II

    I have to work with these types of problems dealing with matrises can someone show me how to solve them.Heres one of them: Directions: Find the values of the variables in each equation in the first matrix it looks like this a+2 3z+1 5m 4k 0 3 then theres a

  41. math

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  42. science

    1 A ……... is a rectangular array of numbers that are enclosed within a bracket . horizontal set vertical matrix 2 When the numbers of rows is equal to the numbers of columns equal to 'n'. Where m=n. Then is called….. a square matrix a column

  43. math

    Prove that if A is a diagonalizable matrix, then the rank of A is the number of nonzero eigenvalues of A. http://ltcconline.net/greenl/courses/203/MatrixOnVectors/symmetricMatrices.htm I've read the entire page and while it's on the correct topic, it

  44. Maths: Algebra Matrices Class 12th

    matrix{{0, 1, -1}, {2, 1, 3}, {1, 1, 1}} matrix{{1, -1, x}} matrix{{0}, {1}, {1}}=0 Find the value of x Don't give me the direct answer. Please tell me how to go about this. Draw in your notebook and then solve

  45. matric

    Let matrix p= [6 -4] 1 0 If where a and b are real numbers, I is a identity matrix and 0 is a null matrix, find a and b.

  46. Math (matrices)

    No one answered my matrix question. Let me rephrase: Let A, B, and 0 be 2x2 matrices. Assuming that A is invertible and 0 is all zeroes, what is the inverse of the matrix [A|0] [B|A] (that is a 4x4 matrix represented as 4 2x2 matrices) The answer is in the

  47. Math

    I have a few questions about T-Matrix. In excel, I am suppose to work with powered matrices to construct a weighted T matrix, using a scalar of .7. Does this mean I multiply each of the powered matrices by .7? Or do I power the powered matrices by .7? Or

  48. MATHS----Matrix

    For a given square matrix A the predicted values of matrix B are: predicted B=A(A'A)^(-1)A'B why is the matrix C=A(A'A)^(-1)A' an idempotent and symmetric matrix? and is this matrix invertible?

  49. Maths - Matrices

    Matrix transformations- please help? let f be the linear transformation represented by the matrix M = (4 2) .......(0 -2) a) state what effect f has on areas and whether it changes orientation b) Find the matrix that represents the inverse of f c) Use the

  50. math

    This is a matrix question. R is the matrix (3r 1) (s 2s) 1. State, in terms of s and r the determinant of R 2. If r=1/3 and s=4 determine the inverse of R 3.State the pair of r and s not including 0, which would make the matrix R a singular matrix

  51. math

    This is a matrix question. R is the matrix (3r 1) (s 2s) 1. State, in terms of s and r the determinant of R 2. If r=1/3 and s=4 determine the inverse of R 3.State the pair of r and s not including 0, which would make the matrix R a singular matrix

  52. algebra

    For problems 13 and 14, assign each letter and a blank space to a number as shown by the alphabet table below. Use the code [1,-2_-3,7] encode the phrase "ONE QUESTION TO GO" The matrix C=[1,-2_-3,7] was used to encode a phrase to

  53. Algebra II

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  54. algebra

    When i have a matrix 4 X 4 and i have to multiply it by a 4 X 3 i know that the product size has to be a 4x 3 so do i do a row times column or how ? It's easiest to learn using the notations for tensors. For any matrix X denote the entry in the i-th row

  55. Math

    Let A, B, and 0 be 2x2 matrices. Assuming that A is invertible, find a matrix C such that [A^-1|0 ] [C |A^-1] is the inverse of the partitioned matrix [A|0] [B|A]

  56. math

    Let A be an orthogonal non-singular matrix of order 'n', then the determinant of matrix 'A-I', i.e., |A-I| (where I is identity matrix) is?

  57. Algebra II (Matrices)

    My book doesn't solve it like a linear equation, they solve it by using inverse matrices. Solve the matrix equation: |4 -5||m|=|32| |1 2| |n|=|-5| A= |4 -5| |1 2| X= |m| |n| B= |32| |-5| Step 1. Find the inverse of the coefficient matrix. A^-1= 1/13|2 5|

  58. Quantitative analysis

    Matrix Algebra Assignment Let A= 4 −1 6 9 and B= 0 3 3 −2 Find: 1. A + B 2. AB 3. BA 4. A' (the transpose of A). 5. What is an Identity Matrix?

  59. Math

    Find the variable for the following 3x3 matrix. |x 3 -1 2 1 -2 4 1 x| Note: This entire matrix =10

  60. Math

    find the values of a and b given that matrix A= [a -4 -6] [-8 5 7] [-5 3 4] is the inverse of matrix B = [1 2 -2] [3 b 1] [-1 1 -3] It would really help if you showed how you did it. Thanks a lot!

  61. quantum

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  62. math 1324

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  63. Math

    A message was encoded using the matrix [7 2 3 1] and you can decode the message 2 numbers at a time in a [1 x 2] matrix. Here are the first four numbers: 66 21 119 35 I know it's coded row matrix times the decoder = the uncoded row matrix. (The key is A=1,

  64. Algebra-Matrix

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  65. algebra

    Hi guys: Can any one please tell me what does this means? Thanks ---------------------------------------------------------------------- The second matrix is simply the symmetric version of the first. This 1 2 3 4 5 6 7 1 0 2 3 x 2 4 x 2 2 3 11 2 3 5 3 3 9

  66. Algebra

    Need help with these-- 40. The graph of the following system yields perpendicular lines: x + 2y = -10 -4y = 2x + 20 True or False? 42. If we multiply a 2 x 2 matrix with a 2 x 1 matrix, the product is a 2 x 1 matrix. -False? Thanks -MC

  67. math

    Let A [ a1, a2, a3] be a 3x3 non-singular matrix, where 1 a ,[a1, a2, a3] are the three columns of A. Define a 3 x 4 matrix B by B[ 2a1+4a2-2a3 , -a1 -4a2 +3a3 ,a2-a3 , 3a1-2a2+6a3] Show that the system of linear equations Bx= b is consistent for every 3 x

  68. matrices

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  69. linear algebra

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  70. Algebra II

    Can someone please help me with this problem. Given Matrix Y= 2 -7 4 and -1 1 0 Matrix Z= 3 4 1 4 2 -4 Solve for matrix X. X-2Y=3X+Z HELP PLEASE!!!

  71. mathematics

    The matrix M = [−3/5 4/5] [4/5 3/5] defines an isometry of the xy-plane. (a)What special properties do the column vectors of this matrix have? (b)Verify that the point (2, 4) remains stationary when M is applied to it. (c)What is the significance of the

  72. Linear Algebra

    Consider the linear transformation T: R^3->R^3 which acts by rotation around the y-axis by an angle of pi, followed by a shear in the x-direction by a factor of 2. a) Find the matrix for T. Explain your method. b) What is T(1,2,3) c) Without calculation,

  73. Algebra2(check part 1)

    1)Solve the matrix:[2x] [14]for x [3y]=[12] answer=7 2)V[3 1] [0 2] [-4 5].The dimensions of matrix V. answer=3x2 3)The first row of T+U T[4 -5 2] U[-9 6 4] [8 -1 3] [-5 -2 3] answer=[-5 1 6] 4)The first row of V-T. V[3 1] T[4 -5 2] [0 2] [8 -1 3] [-4 5]

  74. algebra

    For problems 13 and 14, assign each letter and a blank space to a number as shown by the alphabet table below. Use the code [1,-2_-3,7] encode the phrase "ONE QUESTION TO GO" The matrix C=[1,-2_-3,7] was used to encode a phrase to

  75. math

    hi! Im having trouble with this question about matrices the matrix X = (4 2) (2 4) X to the power of two = 2 (10 8 ) or ...(8 10) 4(5 4) ..(4 5) X to the power of three = 2 (56 52) ...(52 56) or 8 (14 13) .......(13 14) and so on... I have to figure out an

  76. Math

    Construct a graph based on the adjacency matrix that appears below. Label all nodes with indices consistent with the placement of numbers within the matrix. ⌈0 6 0 5 0⌉ | 6 0 1 0 3 | | 0 1 0 4 8 | | 5 0 4 0 0 | ⌊0 3 8 0 0⌋ Describe the graph and

  77. Maths - Matrices

    I'm having trouble with doing this matrix proof The question is "Given some matrix A has the property A*2=A^-1, show that determinant A = 1, i.e |A| = 1" I've tried for ages, but I can't seem to do it, this is what I got to A^2= A^-1 |A^2| = |A^-1| |A|^2 =

  78. Alebra 2

    If the system below were written as a matrix equation, by which matrix could you multiply both sides to obtain a solution? 4x + 6y = 24 5x + 8y = 40

  79. calculus

    hello, if i have the eigenvalues, how can i find the eigenvectors? the current eigenvalues i have include imaginary numbers and i do not have a matrix.

  80. math

    Suppose the matrix A has eigenvalues lambda_1 = -1, lambda_2 = 1, lambda_3 = 2, with corresponding eigenvectors v_1 = [0 5 3]^T, v_2 = [2 0 1]^T, v_3 = [1 -1 0]^T. If you diagonalize A as A = PDP^-1 with P = [2 2 0; p_21 p_22 2; p_31 p_32 p_33], D = [2 0

  81. math-matrices

    You are given the 2x2 matrix M= (k 3) , where k is not 2. (0 2) i)Find the eigenvalues of M, and the corresponding eigenvectos. ii)Express M in the form UDU^(-1), where D is a diagonal matrix. iii)Hence find the matrix M^n.

  82. precalc

    Given a square matrix M, we say that a nonzero vector v is an eigenvector of M if Mv=kv for some real number k. The real number k is called the eigenvalue of v with respect to M. 1. Let v be an eigenvector of the matrix M with eigenvalue k. Find a simple

  83. Maths

    Determine the eigenvalues of the following matrix ( −4 1 −3 0 8 2 0 0 7 )

  84. Differential Equations

    Consider the system shown below of two masses of mass m, coupled together between two fixed walls via springs with varying spring constants. Let x(t) and y(t) be the horizontal displacements of the two masses as a function of time. (a)Write down a system

  85. Math

    Hi! I need help with these two questions. Thanks! :) 1.) Can we multiply the Matrix A (which is 3 x 4 matrix) by the other matrix, Matrix B (which is 3 x 4 matrix)? True Or False? 2.) When we multiply the 6 x 3 matrix by the 3 x 1 matrix, the final matrix

  86. maths

    2 . Put the following macroeconomic model into matrix format using Y, C and T as the variables and find the determinant of the matrix of coefficients. There is no need to solve the equations. Y = C + I C = a + b (Y – T) T = tY Kindly help me with

  87. Differential Equations

    Find the eigenvalues and eigenfunction for the BVP: y ' ' '+ λ2 y ' = 0 , y(0) = 0, y’(0) = 0 and y’(L) = 0

  88. Math

    Fine the size of the following matrix and its additive inverse matrix. Identify if it is a square, column, or row matrix: [ 2 -3 7 1 0 4 ]

  89. Math

    When you are multiplying a 7 x 3 matrix by a 3 x 2 matrix, what would the resulting matrix be of which order? Write your answer is a x b form.

  90. Linear Algebra

    Hi, I really need help with these True/False questions: (a) If three vectors in R^3 are orthonormal then they form a basis in R^3. (b) If Q is square orthogonal matrix such that Q^2018 = I then Q^2017 = Q^T. (c) If B is square orthogonal matrix then B^−1

  91. Pre Calculus

    Find the 2 x 2 matrix A such that pmatrix{(-1,-1)(1 -1)} A = I, where I is the 2 x 2 identity matrix.

  92. Math Check

    Hi! Can someone check this for me? My teacher wants me to write the system of equations that will correspond to the final matrix. I have the matrix already, but I need help with the writing the system stuff. Thanks! Matrix: [-10 2 | 48] [-5 -6/4 |-9] My

  93. Linear Algebra

    Transform the matrix A=[5,−3;1,1], into a matrix B using the similarity transformation (C^−1)AC, with matrix C=[3,1;1,1]. B=(C^−1)AC = ?

  94. matrix, linear transformations

    Morning, Bit confused: I have been given the following: g(x,y)=(4x,6y) h(x,y)=(x+2y,y) k(x,y)=(y,x) and ive got the following matrix for each of them: g={{4,0},{0,6}} h={{1,2},{0,1}} k={{0,1},{1,0}} So ive been asked to prove the linear transformation

  95. Algebra 2.....

    *Please explain on how to do each of these! 1. Let (x) be defined for all positive integer values of x as the product of all even factors of 4x. For example, (3)=12x6x4x2=576. What is the value of (5)? Someone says that it is f(5)= 20x10x2x4=1600 I DO NOT

  96. ALGEBRA 2...

    *Please explain on how to do each of these! 1. Let (x) be defined for all positive integer values of x as the product of all even factors of 4x. For example, (3)=12x6x4x2=576. What is the value of (5)? Someone says that it is f(5)= 20x10x2x4=1600 I DO NOT

  97. Precalculus

    Find the values of x and y. Matrices.. [-4 2 3 5 3 5 2 -3 1] TIMES [2 x 5] EQUALS [9 38 y] It is difficult for me to type the matrices in but.... The first matrix is 3x3 consisting of -4,2,3 in the first row.. 5,3,5 in the second row ......2,-3,1 in the

  98. Matrix, math

    I have matrix A = -1 0 0 -1 B = 0 1 c = 1 0 find n that A^n * matrix B = C find A^2014

  99. Linear Algebra

    Hi, If it asks you to create a 3x3 matrix that spans R^3 so that there is a solution for every b, how do I go about choosing numbers to be in the matrix? Thanks.

  100. Mathematics

    If 1) a b 0 , 2) 0 a b , 3)b 0 a =0, Where 1) ,2),3) represents the three rows of a (3*3) matrix which is equal to 0) show that a/b is the cubic root of (-1). I took b outside the matrix to get, b* {1) (a/b) 1 0 2) 0 (a/b) 1 3) 1 0 (a/b) } I don't see a

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