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explain your answer please 2. Let T:R3 +R be the linear transformation whose standard matrix is...
(1 point) A linear transformation T : R" R whose standard matrix is 1-2 5 -3 6 -23+k is onto if and only if k
Let S be the transformation whose matrix is A, and let T be the transformation whose matrix is followed by S where A and B are the matrices below. Find the matrix C for the transformation resulting from T 7 8 10 10-6 B. A 10 5 -8 -7 0 9 7 0 0 0 C 0 0 0
Lett: R R be a linear transformation whose standard matrix is A = 3 9 . Which of the following 25] statements is true? No work needs to be shown for this question. @ Tis neither one-to-one nor onto Tis onto, but is not one-to-one Tis one-to-one, but is not onto Tis one-to-one and onto
Let x = [X1 X2 X3], and let T:R3 → R3 be the linear transformation defined by x1 + 5x2 – x3 T(x) - X2 x1 + 2x3 Let B be the standard basis for R3 and let B' = {V1, V2, V3}, where 4 4. ---- 4 and v3 -- 4 Find the matrix of T with respect to the basis B, and then use Theorem 8.5.2 to compute the matrix of T with respect to the basis B”....
Let T:R3 + Rbe the linear transformation that projects vectors orthogonally into the vector v = 3 In other words, TⓇ) = proj, Use the formula for projections to compute each of the following: TO) = proj; i = TG) = proj;j = T(K) = proj;k = Use these results to determine the terms of the corresponding matrix A:
Consider the linear transformation T: "R" whose matrix A relative to the standard basis is given. A=[1:2] (a) Find the eigenvalues of A. (Enter your answers from smallest to largest.) (11, 12) = 2,3 |_) (b) Find a basis for each of the corresponding eigenspaces. B = X B2 = = {I (c) Find the matrix A' for T relative to the basis B', where B'is made up of the basis vectors found in part (b). A=
Question 1 (10 points) Let S be the transformation whose matrix is A, and let T be the transformation whose matrix is B, where A and B are the matrices below. Find the matrix C for the transformation resulting from Sfollowed by T. -34 16 -6 -2 A = 2 5 B = 9-1-7 2 0 0 0 0 C = 000 0 0 0
Let x = [xı x2 x3], and let TER → R be the linear transformation defined by T() = x1 + 6x2 – x3 -X2 X1 + 4x3 Let B be the standard basis for R2 and let B' = {V1, V2, V3}, where 7 7 and v3 = 7 V1 V2 [] --[] 0 Find the matrix of I with respect to the basis B. and then use Theorem 8.5.2 to compute the matrix of T with respect to...
Let D be a 2x2 linear transformation matrix that transforms the vector ? = [ 1 4 ] into the vector ?? = [ 3 6 ] and transforms the vector ? = [ 2 5 ] into the vector ?? = [ 0 9 ]. Analyze the linear transformation matrix D by doing the following: Let S be a square with side length 2, located in the xy-plane. The matrix D transforms the vertices of S into the vertices...
(Note: Each problem is worth 10 points). 1. Find the standard matrix for the linear transformation T: that first reflects points through the horizontal L-axis and then reflects points - through the vertical y-axis. 2. Show that the linear transformation T: R - R whose standard [ 2011 matrix is A= is onto but not one-to-one. - R$ whose standard 3. Show that the linear transformation T: R 0 1 matrix is A = 1 1 lov Lool is one-to-one...