![1 -2 1 In exercises 8-1 1 let T : R2[2] → Rİx] have matrix |ー2 1 | with respect 3 1 -3 4 to the basis B = {1 + x, x + 22.2, 2](http://img.homeworklib.com/images/24032f71-4cf4-41ba-b3fd-2cbb7f7f7b70.png?x-oss-process=image/resize,w_560)
let T : R2[x] → R2[x] have
matrix shown in the picture with respect to basis B = {1 + x, x +
2x2, 2 + x − x2}. 8. Compute the image of 2 − 3x + 4x2.
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let T : R2[x] → R2[x] have matrix shown in the picture with respect to basis B = {1 + x, x + 2x2, 2 + x − x2}. 8. Comput...
Exercise 1. Let S(2) = (€1,6) be the standard basis of T R2 and let B...
Exercise 1. Let S(2) = (€1,6) be the standard basis of T R2 and let B = (? =-3e1 + 2e, v2 = 2e1-6). Show that B is a basis of T. Now suppose that a linear mapping f : T T is represented with respect to 8(2) by the matrix oSe 4 6' Find the matrix B that represents f with respect to B.
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...
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...
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) = (5x – y, y - x), B' = {(1, -2), (0, 3)} A' =
Chapter 8, Section 8.5, Question 07 x Incorrect Find the matrix of T with respect to...
Chapter 8, Section 8.5, Question 07 x Incorrect Find the matrix of T with respect to the basis B, and use Theorem 8.5.2 to compute the matrix of T with respect to the basis B . T:R2 R2 is defined by X1- 2x2 X1 T X2 -X2 B = u1, u2} and B = {v1, V2}, where 2 1 V1 = u2 = 1 1 Give exact answer. Write the elements of the matrix in the form of a simple...
Find the matrix A' for T relative to the basis B'. T: R2 R2, 7(x,y) -...
Find the matrix A' for T relative to the basis B'. T: R2 R2, 7(x,y) - (-9x + y, 9x - y), 8' = {(1, -1), (-1,5)} A' 11
1. Let T: R2 – R? be the map "reflection in the line y = x"—you...
1. Let T: R2 – R? be the map "reflection in the line y = x"—you may assume this T is linear, let Eº be the standard basis of R2 and let B be the basis given by B = a) On the graph below, draw a line (colored if possible) joining each of the points each of the points (-). (). (1) and () woits image to its image under the map T. y = x b) Find the...
1. Let L: R2-R2 be defined by L(x.y) (x +2y, 2x - y). Let S be...
1. Let L: R2-R2 be defined by L(x.y) (x +2y, 2x - y). Let S be the natural basis of R2 and let T = {(-1,2), (2,0)) be another basis for R2 . Find the matrix representing L with respect to a) S b) S and1T c) T and S d) T e) Find the transition matrix Ps- from T basis to S basis. f) Find the transition matrix Qre-s from S-basis to T-basis. g) Verify Q is inverse of...
For each transformation T and basis B and C, find the corresponding matrix representation M of...
For each transformation T and basis B and C, find the corresponding matrix representation M of T from basis B to basis C. 1) Let T6 = la + 2b + 4c 3a +86 + 16c la + 3b + 6c be a linear transformation. -2a +(-7) + (-14)c] с 1 Let B= 2 > -1 4 0 2 Let C = [11] [32] [] [1] The matrix M for transformation T from basis B to C would be: 2)...
3. Let T : R2 + Rº be the rotation by 1/2 clockwise about the origin,...
3. Let T : R2 + Rº be the rotation by 1/2 clockwise about the origin, and let S : R2 + R2 be the shear along the y-axis given by S(x,y) = (x,x+y). (You may assume that these are linear transformations.) (a) Write down, or compute, the standard matrix representations of T and S. (b) Use (a) to find the standard matrix representations of (i) SoT (T followed by S), and (ii) ToS (S followed by T). (c) Let...
Exercise 1. Let S(2) = (€1,6) be the standard basis of T R2 and let B = (? =-3e1 + 2e, v2 = 2e1-6). Show that B is a basis of T. Now suppose that a linear mapping f : T T is represented with respect to 8(2) by the matrix oSe 4 6' Find the matrix B that represents f with respect to B.
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...
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...
Find the matrix A' for T relative to the basis B'. T: R2 → R2, T(x, y) = (5x – y, y - x), B' = {(1, -2), (0, 3)} A' =
Chapter 8, Section 8.5, Question 07 x Incorrect Find the matrix of T with respect to the basis B, and use Theorem 8.5.2 to compute the matrix of T with respect to the basis B . T:R2 R2 is defined by X1- 2x2 X1 T X2 -X2 B = u1, u2} and B = {v1, V2}, where 2 1 V1 = u2 = 1 1 Give exact answer. Write the elements of the matrix in the form of a simple...
Find the matrix A' for T relative to the basis B'. T: R2 R2, 7(x,y) - (-9x + y, 9x - y), 8' = {(1, -1), (-1,5)} A' 11
1. Let T: R2 – R? be the map "reflection in the line y = x"—you may assume this T is linear, let Eº be the standard basis of R2 and let B be the basis given by B = a) On the graph below, draw a line (colored if possible) joining each of the points each of the points (-). (). (1) and () woits image to its image under the map T. y = x b) Find the...
1. Let L: R2-R2 be defined by L(x.y) (x +2y, 2x - y). Let S be the natural basis of R2 and let T = {(-1,2), (2,0)) be another basis for R2 . Find the matrix representing L with respect to a) S b) S and1T c) T and S d) T e) Find the transition matrix Ps- from T basis to S basis. f) Find the transition matrix Qre-s from S-basis to T-basis. g) Verify Q is inverse of...
For each transformation T and basis B and C, find the corresponding matrix representation M of T from basis B to basis C. 1) Let T6 = la + 2b + 4c 3a +86 + 16c la + 3b + 6c be a linear transformation. -2a +(-7) + (-14)c] с 1 Let B= 2 > -1 4 0 2 Let C = [11] [32] [] [1] The matrix M for transformation T from basis B to C would be: 2)...
3. Let T : R2 + Rº be the rotation by 1/2 clockwise about the origin, and let S : R2 + R2 be the shear along the y-axis given by S(x,y) = (x,x+y). (You may assume that these are linear transformations.) (a) Write down, or compute, the standard matrix representations of T and S. (b) Use (a) to find the standard matrix representations of (i) SoT (T followed by S), and (ii) ToS (S followed by T). (c) Let...
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