Linear Transformations

Welcome to the "Linear Transformations" category on Questions LLC! If you're a math enthusiast or just eager to learn more about linear transformations, you've come to the right place. In this category, you will find a plethora of questions related to linear transformations, a fundamental concept in linear algebra. Whether you're curious about the theory behind linear transformations, their applications in various fields, or how to perform calculations involving them, our community of experts and enthusiasts are here to provide you with insightful answers. So, dive into this category and expand your knowledge on linear transformations today!

Questions (35)

Suppose T: ℝ2→ℝ3 is a linear transformation. Let U, V and W be the vectors given below, and suppose that T(U) and T(V) are
1. 2 answers
2. asked by Big L
3. 556 views
Let T:R3 →R 3 be a linear transformation such that T(1,0,0)=(2,−1,4),T(0,1,0)=(1,−2,3), and T(0,0,1)=(2,−2,0). Find the
1. 2 answers
2. asked anonymously
3. 52 views
Matrix transformations- please help?let f be the linear transformation represented by the matrix M = (4 2) .......(0 -2) a)
1. 1 answer
2. asked by Anonymous
3. 716 views
LetL: R2 �¨ R2 be a linear transformation for which we know that L(1 1)= [-2 1] L(-1 1)=[3 2] a)what is L(-1 5) b)what is L(u
1. 4 answers
2. asked by hannah
3. 1,561 views
Suppose T: ℝ3→ℝ2 is a linear transformation. Let U and V be the vectors given below, and suppose that T(U) and T(V) are as
1. 4 answers
2. asked by Big L
3. 452 views
Let f : R → R3 be deﬁned by f(x) = <4x,−3x,5x+5>. Is f a linear transformation
1. 4 answers
2. asked by Sam
3. 2,196 views
(a) Let [r s] ∈R^2 and T: R2→R2 be defined by T(⃗u)=⃗u+ [r s].Show that if r /= 0 or s/=0 thenT is not a linear
1. 1 answer
2. asked by David
3. 371 views
Let L be the line y=mx in R2 and u= [1 m] . Let Qm be the linear transformation that reflects a vector over L.(a) Show that
1. 0 answers
2. asked by marc
3. 574 views
1. LetT :R3→R3 . Show that ifT ([c1 c2 c3]) = c1T ([1 0 0]) + c2T([0 1 0]) + c3T ([0 0 1]) for c1, c2, c3 ∈ R then T
1. 1 answer
2. asked by Ally
3. 671 views
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
1. 3 answers
2. asked by Anon
3. 500 views
Hello, can anyone give me some help with these excersises?1. Give an example of a linear transformation that is injective but
1. 1 answer
2. asked by Linear Algebra
3. 418 views
Construct a 2 × 2 matrix that defines a shear of factor 4 in the y-direction, followed by a scaling of factor 5 in the
1. 1 answer
2. asked by Asad
3. 410 views
Determine the standard matrix A of the linear mapping L:R^2-->R^2 that rotates any vector through an angle of 150 degrees in the
1. 1 answer
2. asked by John
3. 438 views
Determine the standard matrix D of the linear mapping G: R^2--R^2 that first rotates points clockwise through pi/6 radians and
1. 1 answer
2. asked by John
3. 410 views
2. Suppose that T is a linear transformation from R2 to R4such that T ((1, 1)) = (3, −1, 4, −3) and T ((2, −1)) = (3,
1. 0 answers
2. asked by Ryan
3. 912 views
Consider the left shift operator on the space of infinite sequences of complex numbers:L(z1,z2,…)=(z2,z3,…). Is L injective?
1. 1 answer
2. asked by JuanPro
3. 480 views
Suppose T: R^2->R^2 is a linear transformation with T(1,2)=(2,-1) & T(3,-1)=(-1,2). What is T(-12,11)?
1. 2 answers
2. asked by Brody
3. 591 views
Use the linear transformation model to predict the number of fish in 12 monthslog y = 0.9013.logx+ 0.6935
1. 3 answers
2. asked by helen
3. 482 views
find the linear transformation model of log y^ = 0.6021x + 0.4771.
1. 3 answers
2. asked by helen
3. 508 views
Let V and W be vector spaces over a field and let T:V->W be a linear transformation then V/kerT =R(T)(A) True (B) False (C)
1. 1 answer
2. asked by Sower II
3. 340 views
(1) Define T:R->R be a linear transformation such that T(x,y,z)= (2x,2y,2z) then the given value of T isA. 3 B. 2 C. 4 D. 6 (A)
1. 1 answer
2. asked by Sower
3. 641 views
Show that the transformation T:R^2->R^2 given T(x1,x2)=(3x1-5x2,x1+2x2)is linear by verifying that satisfies the definition of
1. 1 answer
2. asked by Jason
3. 699 views
Can you check my calculations pleaseg maps points (0,0),(1,0),(0,1) to (6,-2),(6,-1),(5,-2) So, g(x) = (0 -1) .....(6)
1. 1 answer
2. asked by Anonymous
3. 332 views
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. 1 answer
2. asked by mathstudent
3. 492 views
For the transformation T, what is T-1?T : (x, y) (x + 4, y + 3) T-1: (x, y)
1. 2 answers
2. asked by robbie
3. 914 views
Determine whether or not the given linear transformation is invertible. If it is invertible, compute its inverse. (If the
1. 2 answers
2. asked by Peter
3. 788 views
The transformation T:R^2--》R^2 is defined by T(1,0)=(2,-5) and T(-3,2)=(1,4). Find the natural matrix of the linear
1. 1 answer
2. asked by Phil
3. 612 views
Can someone please help me with this question. Thank you!State the image of the given point after the following transformation:
1. 2 answers
2. asked by Katie
3. 592 views
Consider the transformation T:x=(41/40)u−(9/41)v , y=(9/41)u+(40/41)vA. Computer the Jacobian: delta(x,y)/delta(u,v)= ? B. The
1. 1 answer
2. asked by Salman
3. 510 views
For each of the following linear transformations, write down its matrix and describe the transformationa) g(x,y)=(4x,6y) b)
1. 1 answer
2. asked by s17
3. 510 views
The line y = x is transformed to create the liney = − 1 2 x − 1 . Which of the following may be used to describe the
1. 2 answers
2. asked by earth
3. 461 views
Let f be the linear transformation represented by the matrixA=(-2 3 4 -4) a=-2, b=3, c=4, d=-4 Find the point (x,y) such that
1. 2 answers
2. asked by s17
3. 500 views
show that each function is a linear tranformation T(x,y)=(2x,x+y,x-2y) (T:R²=>r³)(2) T:R³=>M^(2,2) given by T(x,y,z)=[y 2] [2
1. 4 answers
2. asked by clement
3. 428 views
Give a point on a line segment (-4, 5), what is the new point when the point is rotated counterclockwise about the origin 270
1. 1 answer
2. asked by aaa
3. 245 views
Describe the transformation from LAP to L’A’P’.A. Translation 1 unit right and 3 units down. B. Reflection over the
1. 3 answers
2. asked anonymously
3. 27 views