Question

Consider the transformation T: R2 -> R3 defined by T(x,y) = (x-y,x+y,x+2y) Answer the Following a)Find...

Consider the transformation T: R2 -> R3 defined by

T(x,y) = (x-y,x+y,x+2y)

Answer the Following

a)Find the Standard Matrix A for the linear transformation

b)Find T([1

-2])

c) determine if c = [0 is in the range of the transformation T

2

3]

Please explain as much as possible this is a test question that I got no points on. Now studying for the final and trying to understand past test questions.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Assume that T is a linear Transformation. a) Find the Standard matrix of T is T:...
Assume that T is a linear Transformation. a) Find the Standard matrix of T is T: R2 -> R3 first rotate point through (pie)/2 radian (counterclock-wise) and then reflects points through the horizontal x-axis b) Use part a to find the image of point (1,1) under the transformation T Please explain as much as possible. This was a past test question that I got no points on. I'm study for the final and am trying to understand past test questions.
Let T be the function from R2 to R3 defined by T ( (x,y) ) =...
Let T be the function from R2 to R3 defined by T ( (x,y) ) = (x, y, 0). Prove that T is a linear transformation, that it is 1-1, but that it is not onto.
(12) (after 3.3) (a) Find a linear transformation T : R2 → R2 such that T...
(12) (after 3.3) (a) Find a linear transformation T : R2 → R2 such that T (x) = Ax that reflects a vector (x1, x2) about the x2-axis. (b) Find a linear transformation S : R2 → R2 such that T(x) = Bx that rotates a vector (x1, x2) counterclockwise by 135 degrees. (c) Find a linear transformation (with domain and codomain) that has the effect of first reflecting as in (a) and then rotating as in (b). Give the...
Consider the matrix transformation T(x,y,z) = (-x+y+z, 2x-y, 18x+y+ 18z) from R3 to R3 Then the...
Consider the matrix transformation T(x,y,z) = (-x+y+z, 2x-y, 18x+y+ 18z) from R3 to R3 Then the sum of the elements of the last row of the standard matrix of T is
3. Find the linear transformation T : R2 → R2 described geometrically by “first rotate coun-...
3. Find the linear transformation T : R2 → R2 described geometrically by “first rotate coun- terclockwise by 60◦, then reflect across the line y = x, then scale vectors by a factor of 5”. Is this linear transformation invertible? If so, find the matrix of the inverse transformation.
3.) Find the linear transformation T : R2 to R2 described geometrically by "first rotate counter-clockwise...
3.) Find the linear transformation T : R2 to R2 described geometrically by "first rotate counter-clockwise by 60 degrees, then reflect across the line y = x, then scale vectors by a factor of 5". Is this linear transformation invertible? If so, find the matrix of the inverse transformation.
Let T be the linear transformation from R2 to R2, that rotates a vector clockwise by...
Let T be the linear transformation from R2 to R2, that rotates a vector clockwise by 60◦ about the origin, then reflects it about the line y = x, and then reflects it about the x-axis. a) Find the standard matrix of the linear transformation T. b) Determine if the transformation T is invertible. Give detailed explanation. If T is invertible, find the standard matrix of the inverse transformation T−1. Please show all steps clearly so I can follow your...
(1) Consider the linear operator T : R2 ! R2 defined by T x y =...
(1) Consider the linear operator T : R2 ! R2 defined by T x y = 117x + 80y ??168x ?? 115y : Compute the eigenvalues of this operator, and an eigenvector for each eigen-
(a) Let T be any linear transformation from R2 to R2 and v be any vector...
(a) Let T be any linear transformation from R2 to R2 and v be any vector in R2 such that T(2v) = T(3v) = 0. Determine whether the following is true or false, and explain why: (i) v = 0, (ii) T(v) = 0. (b) Find the matrix associated to the geometric transformation on R2 that first reflects over the y-axis and then contracts in the y-direction by a factor of 1/3 and expands in the x direction by a...
10 Linear Transformations. Let V = R2 and W = R3. Define T: V → W...
10 Linear Transformations. Let V = R2 and W = R3. Define T: V → W by T(x1, x2) = (x1 − x2, x1, x2). Find the matrix representation of T using the standard bases in both V and W 11 Let T :R3 →R3 be a linear transformation such that T(1, 0, 0) = (2, 4, −1), T(0, 1, 0) = (1, 3, −2), T(0, 0, 1) = (0, −2, 2). Compute T(−2, 4, −1).
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT