![Let 9 - {(1,3), (-2,-2)) and 8 = {(-12, 0),(-4,4) be bases for R, and let --12:] be the matrix for T. R2 + R2 relative to B.](http://img.homeworklib.com/questions/bc64dfe0-ee73-11ea-b54f-fffd85c46ee4.png?x-oss-process=image/resize,w_560)
Homework Answers
![8= {(1,2).(-2,-2)] B= {(-12,0), C-4,4 33 23 a) (-12,0) = a[1,37 +66-2-2) a-ab=-12 3a-ab=0 Qa=-12 a=](http://img.homeworklib.com/questions/816f0f90-ee77-11ea-b324-01e329c40c0d.png?x-oss-process=image/resize,w_560)
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![T 473 15a 2 d) [Tiva] - [Tinja JE 28 -41 (½ ½ 3/4-1/2 13/3 L-1/2 [v]el i 4/3 152 2 F13/3 Five So JE 1-1/](http://img.homeworklib.com/questions/82d64d40-ee77-11ea-9cb5-89b8630d3a7e.png?x-oss-process=image/resize,w_560)
a)
for finding P we express each vector in basis B' as a linear
combination of vectors in basis B.
then using that coefficients we write P
we do another parts step by step above.
Add Answer to:
Let 9 - {(1,3), (-2,-2)) and 8 = {(-12, 0),(-4,4) be bases for R, and let...
{(1,3), (2,-2)} and B = {(-12,0), (-4, 4)} be the basis for R2 and let A...
{(1,3), (2,-2)} and B = {(-12,0), (-4, 4)} be the basis for R2 and let A = 7. Let B 3 2 0 4 be the matrix for T R2 -> R2 relative to B (a) Find the transition matrix P from B' to B (b) Use the matrices A and P to find [v]B and [T(v)]B where v] 2 (c) Find P and A' (the transition matrix for T relative to B') (d) Find [T(v)B' in two ways: first...
Find the matrix A' for T relative to the basis B'. T: R2 + R2, T(x,...
Find the matrix A' for T relative to the basis B'. T: R2 + R2, T(x, y) = (3x - y, 4x), B' = {(-2, 1), (-1, 1)} A' = Let B = {(1, 3), (-2,-2)} and B' = {(-12, 0), (-4,4)} be bases for R2, and let 0 2 A = 3 4 be the matrix for T: R2 + R2 relative to B. (a) Find the transition matrix P from B' to B. 6 4 P= 9 4...
Let B = {(1,0), (0, 1)} and B' = {(0, 1), (1, 1)} be two bases...
Let B = {(1,0), (0, 1)} and B' = {(0, 1), (1, 1)} be two bases for the vector space V = RP. Moreover, let [y]g = [1 -2]" and the matrix for T relative to B be 2 A= 22 -2 2. (a) Find the transition matrix P from B' to B. (b) Use the matrices P and A to find [v] and [T(0) В" (C) Find A' (the matrix for T relative to B'). (d) Find (T(m)]g
2) Let B = {(1, 3, 4), (2,-5,2), (-4,2-6)) and B/-(( 1, 2,-2), (4, 1,-4), (-2, 5, 8)) be 5 ordered bases of R2. Let x = | 8 | in the standard basis of R2. a) Use a matrix and x to find L18 ]B. b) U...
2) Let B = {(1, 3, 4), (2,-5,2), (-4,2-6)) and B/-(( 1, 2,-2), (4, 1,-4), (-2, 5, 8)) be 5 ordered bases of R2. Let x = | 8 | in the standard basis of R2. a) Use a matrix and x to find L18 ]B. b) Use a matrix and [X]B to find [x)B/. c) Use a matrix and [X]B/ to find x in the standard basis of R2, d) Draw a diagram of the steps a), b), and...
2 question ---------------------------------------------------------- (1 point) Consider the ordered bases B =( (8-4] [: • and c-...
2 question
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(1 point) Consider the ordered bases B =( (8-4] [: • and c- (- -)( :} ) for the vector space V of lower triangular 2 x 2 matrices with zero trace. a. Find the transition matrix from C to B. TB = b. Find the coordinates of Min the ordered basis B if the coordinate vector of Min C is [Mc= [MB = C. Find M. M= (1 point) Consider the ordered bases B [ 1...
(2) Let T: P2 + R2 be given by T(p) = [pc] (e.g. if p= a...
(2) Let T: P2 + R2 be given by T(p) = [pc] (e.g. if p= a + bx, then p(4) = a + b(4) = a + 4b.) (a) Find the matrix of T relative to the standard bases B = {1, 2,2} of P2, and C = {ej,ez} of R (b) Find the matrix of T relative to the basis A = {1, 1+,1+x+x?} of P2 and D= {(1, 1), (1, -1)} of R2 (c) Find a basis for...
linear algebra Let V (71, 72, 3}, where 71 73=(2,0,3). (1,3,-1), 2 = (0, 1,4), and...
linear algebra
Let V (71, 72, 3}, where 71 73=(2,0,3). (1,3,-1), 2 = (0, 1,4), and (a) Prove: V is a basis. (b) Find the coordinates of (b, b2, bs) with respect to V = {71, U2, 3,}. (c) Suppose M and M' are matrices whose columns span the same vector space V. Let b be the coordinates of relative to M. Write a matrix equation that gives b', the coordinates of relative to M'. (Your answer should be a...
5. Let T: P2(R) + RP be the linear transformation that has the matrix …_…………..ນະ 1...
5. Let T: P2(R) + RP be the linear transformation that has the matrix …_…………..ນະ 1 2 -1 11 1 1 relative to the bases a = 1+ 21,1+1+12,1+for P2 (R) and B = (1,1),(1,-1) for R2. Find the matrix of T relative to the bases d' = 2+3.r,1+1+12,2+3.+r2 for P2(R) and B' =(3,-1),(1,-1) for R2.
Let matrix M = -8 -24 -12 0 4 0 6 12 10 (a) Find the...
Let matrix M = -8 -24 -12 0 4 0 6 12 10 (a) Find the eigenvalues of M (b) For each eigenvalue λ of M, find a basis for the eigenspace of λ. (c) Is the matrix M diagonalizable? If so, find matrices D and P such that D is a diagonal matrix and M=PDP^−1. If not, explain carefully why not.
Let matrix M = -8 -24 12 0 4 0 6 12 10 (a) Find the...
Let matrix M = -8 -24 12 0 4 0 6 12 10 (a) Find the eigenvalues of M (b) For each eigenvalue λ of M, find a basis for the eigenspace of λ. (c) Is the matrix M diagonalizable? If so, find matrices D and P such that D is a diagonal matrix and M=PDP−1. If not, explain carefully why not.
{(1,3), (2,-2)} and B = {(-12,0), (-4, 4)} be the basis for R2 and let A = 7. Let B 3 2 0 4 be the matrix for T R2 -> R2 relative to B (a) Find the transition matrix P from B' to B (b) Use the matrices A and P to find [v]B and [T(v)]B where v] 2 (c) Find P and A' (the transition matrix for T relative to B') (d) Find [T(v)B' in two ways: first...
Find the matrix A' for T relative to the basis B'. T: R2 + R2, T(x, y) = (3x - y, 4x), B' = {(-2, 1), (-1, 1)} A' = Let B = {(1, 3), (-2,-2)} and B' = {(-12, 0), (-4,4)} be bases for R2, and let 0 2 A = 3 4 be the matrix for T: R2 + R2 relative to B. (a) Find the transition matrix P from B' to B. 6 4 P= 9 4...
Let B = {(1,0), (0, 1)} and B' = {(0, 1), (1, 1)} be two bases for the vector space V = RP. Moreover, let [y]g = [1 -2]" and the matrix for T relative to B be 2 A= 22 -2 2. (a) Find the transition matrix P from B' to B. (b) Use the matrices P and A to find [v] and [T(0) В" (C) Find A' (the matrix for T relative to B'). (d) Find (T(m)]g
2) Let B = {(1, 3, 4), (2,-5,2), (-4,2-6)) and B/-(( 1, 2,-2), (4, 1,-4), (-2, 5, 8)) be 5 ordered bases of R2. Let x = | 8 | in the standard basis of R2. a) Use a matrix and x to find L18 ]B. b) Use a matrix and [X]B to find [x)B/. c) Use a matrix and [X]B/ to find x in the standard basis of R2, d) Draw a diagram of the steps a), b), and...
2 question
----------------------------------------------------------
(1 point) Consider the ordered bases B =( (8-4] [: • and c- (- -)( :} ) for the vector space V of lower triangular 2 x 2 matrices with zero trace. a. Find the transition matrix from C to B. TB = b. Find the coordinates of Min the ordered basis B if the coordinate vector of Min C is [Mc= [MB = C. Find M. M= (1 point) Consider the ordered bases B [ 1...
(2) Let T: P2 + R2 be given by T(p) = [pc] (e.g. if p= a + bx, then p(4) = a + b(4) = a + 4b.) (a) Find the matrix of T relative to the standard bases B = {1, 2,2} of P2, and C = {ej,ez} of R (b) Find the matrix of T relative to the basis A = {1, 1+,1+x+x?} of P2 and D= {(1, 1), (1, -1)} of R2 (c) Find a basis for...
linear algebra
Let V (71, 72, 3}, where 71 73=(2,0,3). (1,3,-1), 2 = (0, 1,4), and (a) Prove: V is a basis. (b) Find the coordinates of (b, b2, bs) with respect to V = {71, U2, 3,}. (c) Suppose M and M' are matrices whose columns span the same vector space V. Let b be the coordinates of relative to M. Write a matrix equation that gives b', the coordinates of relative to M'. (Your answer should be a...
5. Let T: P2(R) + RP be the linear transformation that has the matrix …_…………..ນະ 1 2 -1 11 1 1 relative to the bases a = 1+ 21,1+1+12,1+for P2 (R) and B = (1,1),(1,-1) for R2. Find the matrix of T relative to the bases d' = 2+3.r,1+1+12,2+3.+r2 for P2(R) and B' =(3,-1),(1,-1) for R2.
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