Let B = {(1 2),(3 5)} and B'= {(1-1),(1-2)} be two bases of R2. Also, let...
- Let B = {(1 2),(3 5)} and B'= {(1-1),(1-2)} be two bases of R2. Also, let TB: R2→R2 be a linear operator on B described as TB(x,y) = (x+2y,x+y). Find TB'.
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Let B = {(1
2),(3 5)} and
B'=
{(1-1),(1-2)} be
two bases of R2. Also, let...
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...
Problem 2 [10pts] Let f : R3 + R2 be a linear transformation given by f((x,...
Problem 2 [10pts] Let f : R3 + R2 be a linear transformation given by f((x, y, z) = (–2x + 2y +z, -x +2y). Find the matrix that corresponds to f with respect to the canonical bases of R3 and R2.
Given bases B = {(2,-3).(5,4)} and B' = {(1,0),(0, 1)) for R2 and coordinate matrix [3]...
Given bases B = {(2,-3).(5,4)} and B' = {(1,0),(0, 1)) for R2 and coordinate matrix [3] * [8] + [6] find the following two things. The transition matrix from B to B' The coordinate matrix x[*],
Let V = P1(R) and W = R2. Let B = (1,x) and y=((1,0), (0, 1))...
Let V = P1(R) and W = R2. Let B = (1,x) and y=((1,0), (0, 1)) be the standard ordered bases for V and W respectively. Define a linear map T:V + W by T(P(x)) = (p(0) – 2p(1), p(0) + p'(0)). (a) Let FEW* be defined by f(a,b) = a – 26. Compute T*(f). (b) Compute [T]y,ß and (T*]*,y* using the definition of the matrix of a linear transformation.
Let L : R2 → R3 be a linear transformation such that L 1 1 =...
Let L : R2 → R3 be a linear transformation such that L 1 1 = 1 2
3 and L 1 2 = 2 1 3 . Find L 2 1 Find the standard matrix
representing L. Find the dimensions of the kernel and the range of
L and their bases.
12. Let L : R² + RP be a linear transformation such that L | (3) - -(5)-(1) Find I (*) Find the standard matrix representing L. Find...
Linear algebra Chapter 8, Section 8.2, Question 22b Let T1:R2 → R2 and T2:R2 → R2...
Linear algebra
Chapter 8, Section 8.2, Question 22b Let T1:R2 → R2 and T2:R2 → R2 be the linear operators given by the formulas T1(x, y) = (x + y, x - y) and T2(x, y) = (2x + y, x - 2y) Find formulas for Tīl(x, y), , Tz?(x, y), , and (T2• Tı) (x, y). Tīl(x, y) = Edit T'(x,y) (0,5 Edit (T2T1)-1(x, y) = Edit Click if you would like to Show Work for this question: Open...
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...
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...
0o 5. (a) (10) Let f(x), and assume that the radius of convergence of the power series is 3. Find the radius of convergence R2 for f"() Also find the appropriate power series for f"(2)....
0o 5. (a) (10) Let f(x), and assume that the radius of convergence of the power series is 3. Find the radius of convergence R2 for f"() Also find the appropriate power series for f"(2). (b) (10) Let z 16i. Find a formula for each of the two square roots z0, 31 of z. Graph both square roots in the complex plane, and identify each.
0o 5. (a) (10) Let f(x), and assume that the radius of convergence of the...
11. Suppose S: R R2 is the linear transformation with matrix -3 11 [2 -6 2 relative to the bases & and &. Fi...
11. Suppose S: R R2 is the linear transformation with matrix -3 11 [2 -6 2 relative to the bases & and &. Find the matrix of S with respect to the bases (1,0, 1), (1,0,0), (1, 1,0)) and ((1,-1). (2,0).
11. Suppose S: R R2 is the linear transformation with matrix -3 11 [2 -6 2 relative to the bases & and &. Find the matrix of S with respect to the bases (1,0, 1), (1,0,0), (1, 1,0)) and...
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...
Problem 2 [10pts] Let f : R3 + R2 be a linear transformation given by f((x, y, z) = (–2x + 2y +z, -x +2y). Find the matrix that corresponds to f with respect to the canonical bases of R3 and R2.
Given bases B = {(2,-3).(5,4)} and B' = {(1,0),(0, 1)) for R2 and coordinate matrix [3] * [8] + [6] find the following two things. The transition matrix from B to B' The coordinate matrix x[*],
Let V = P1(R) and W = R2. Let B = (1,x) and y=((1,0), (0, 1)) be the standard ordered bases for V and W respectively. Define a linear map T:V + W by T(P(x)) = (p(0) – 2p(1), p(0) + p'(0)). (a) Let FEW* be defined by f(a,b) = a – 26. Compute T*(f). (b) Compute [T]y,ß and (T*]*,y* using the definition of the matrix of a linear transformation.
Let L : R2 → R3 be a linear transformation such that L 1 1 = 1 2
3 and L 1 2 = 2 1 3 . Find L 2 1 Find the standard matrix
representing L. Find the dimensions of the kernel and the range of
L and their bases.
12. Let L : R² + RP be a linear transformation such that L | (3) - -(5)-(1) Find I (*) Find the standard matrix representing L. Find...
Linear algebra
Chapter 8, Section 8.2, Question 22b Let T1:R2 → R2 and T2:R2 → R2 be the linear operators given by the formulas T1(x, y) = (x + y, x - y) and T2(x, y) = (2x + y, x - 2y) Find formulas for Tīl(x, y), , Tz?(x, y), , and (T2• Tı) (x, y). Tīl(x, y) = Edit T'(x,y) (0,5 Edit (T2T1)-1(x, y) = Edit Click if you would like to Show Work for this question: Open...
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...
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...
0o 5. (a) (10) Let f(x), and assume that the radius of convergence of the power series is 3. Find the radius of convergence R2 for f"() Also find the appropriate power series for f"(2). (b) (10) Let z 16i. Find a formula for each of the two square roots z0, 31 of z. Graph both square roots in the complex plane, and identify each.
0o 5. (a) (10) Let f(x), and assume that the radius of convergence of the...
11. Suppose S: R R2 is the linear transformation with matrix -3 11 [2 -6 2 relative to the bases & and &. Find the matrix of S with respect to the bases (1,0, 1), (1,0,0), (1, 1,0)) and ((1,-1). (2,0).
11. Suppose S: R R2 is the linear transformation with matrix -3 11 [2 -6 2 relative to the bases & and &. Find the matrix of S with respect to the bases (1,0, 1), (1,0,0), (1, 1,0)) and...
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