Question

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).

Engineering   Electrical-Engineering   
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
Let V = W = R2. Choose the basis B = {x1, x2} of V ,...
Let V = W = R2. Choose the basis B = {x1, x2} of V , where x1 = (2, 3), x2 = (4,−5) and choose the basis D = {y1,y2} of W, where y1 = (1,1), y2 = (−3,4). Find the matrix of the identity linear mapping I : V → W with respect to these bases.
(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...
1) Let T : V —> W be a linear transformation with dim(V) = m and...
1) Let T : V —> W be a linear transformation with dim(V) = m and dim(W) = n. For which of the following conditions is T one-to-one? (A) m>n (B) range(T)=Wandm=n (C) nullity(T) = m (D) rank(T)=m-1andn>m 2) For which of the linear transformations is nullity (T) = 0 ? Why? (A)T:R3 —>R8 (B)T:P3 —>P3 (C)T:M23 —>M33 (D)T:R5 —>R2 withrank(T)=2 withrank(T)=3 withrank(T)=6 withrank(T)=1
Let T ∈ L(R2) be the linear transformation T(x1, x2) = (3x1 + 2x2, −4x1 −...
Let T ∈ L(R2) be the linear transformation T(x1, x2) = (3x1 + 2x2, −4x1 − 3x2), v = (1, −1), and p(z) = z^2 − 3z + 2. Compute p(T), show that p(T)v = 0, and show that NOT all the roots of p(z) are eigenvalues of T.
(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...
Let the linear transformation T: V--->W be such that T (u) = u2 If a, b...
Let the linear transformation T: V--->W be such that T (u) = u2 If a, b are Real. Find T (au + bv) , if u = (x, y) v = (z, w) and uv = (xz-yw, xw + yz) Let the linear transformation T: V---> W be such that T (u) = T (x, y) = (xy, 0) where u = (x, y), with 2, -3. Then, if u = ( 1.0) and v = (0.1). Find the value...
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.
Let V1 = R4 and V2 = R2. Let T : V1 → V2 be the...
Let V1 = R4 and V2 = R2. Let T : V1 → V2 be the map dened by T x1 x2 x3 x4 = x1 −x2 + x4 x1 + x2 + x3 + x4 . (a) Show that T is a linear transformation. (b) Let u1 = 1 0 0 −1 , u2 = 0 1 −2 1 .Show that ( u1, u2) is a basis of kerT. (c) Show that imT = V2. (Hint: Compute T(e1) and...
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...
Find the coordinates of e1 e2 e3 of R3 in terms of [(1,0,0)T , (1,1,0)T ,...
Find the coordinates of e1 e2 e3 of R3 in terms of [(1,0,0)T , (1,1,0)T , (1,1,1)T ] of R3,, and then find the matrix of the linear transformation T(x1,, x2 , x3 )T = [(4xx+ x2- x3)T , (x1 + 3x3)T , (x2 + 2x3)T with respect to this basis.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT