Maths - Matrices

posted by .

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 matrix you found in part b to find the image f(c) of the unit circle C under f , in the form

ax^2 + bxy + cy^2 = d

where a, b, c, d are integers

d) what is the area enclosed by f(c)?


My answers;

a)det M = (4*-2) - (2*0) = -8 so f scales areas by factor 8 and changes orientation

b) m^-1 = 1/-8 (-2 -2) ... (1/4 1/4)
..............=..............o 4) = (0 -1/2)


c) 1/16x^2 + 2/16xy + 1/16y^2 = 1
which is;

x^2 + 2xy + y^2 = 16

(ive struggled with this one so if its wrong i would appreciate some help with my working out)

d) the area enclosed by f(C) is 16pi


Thanks

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. linear algebra

    if: A and B are matrices and A^2 is similar to B^2 Is A guaranteed to be similar to B?
  2. 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?
  3. 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
  4. 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) …
  5. Linear Algebra

    2. Suppose that T is a linear transformation from R2 to R4 such that T ((1, 1)) = (3, −1, 4, −3) and T ((2, −1)) = (3, −2, −1, −3). Determine the matrix of T (with respect to the standard bases). …
  6. Linear Algebra

    Diagonalize the matrix A = [1,1;-2,4] using a similarity transformation. Give the transformation matrices such that (C^−1)AC = D, where D is a diagonal matrix. (D, C) = ?
  7. Linear Algebra

    Diagonalize the matrix A = [1,1;-2,4] using a similarity transformation. Give the transformation matrices such that (C^−1)AC = D, where D is a diagonal matrix. (D, C) = ?
  8. maths

    Let f be the linear transformation represented by the matrix A=(-2 3 4 -4) a=-2, b=3, c=4, d=-4 Find the point (x,y) such that f(x,y)=(4,4)
  9. maths

    For each of the following linear transformations, write down its matrix and describe the transformation a) g(x,y)=(4x,6y) b) h(x,y)=(x+2y,y) c) k(x,y)=(y,x) so I have worked out the matrices: (4 0 0 6) (1 2 0 1) (0 1 1 0) Not sure …
  10. 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 …

More Similar Questions