Only part C please. Problem #1: Let T: P2 → P3 be the linear transformation defined...
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 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”....
1 -1.2 5 Uį = U2 = -3 1, U3 = 2 , 14 = 29 ( 7 Answer the following questions and give proper explanations. (a) Is {ui, U2, uz} a basis for R3? (b) Is {ui, U2, u4} a basis for R4? (c) Is {ui, U2, U3, U4, u; } a basis for R? (d) Is {ui, U2, U3, u} a basis for Rº?! (e) Are ui, u, and O linearly independent?! Problem 6. (15 points). Let A...
I am looking for how to explain #4 part b. I have gotten the matrix A and I believe the answer is W = span{ v1 u2 u3 } however I'm not really sure if that is correct or not. Please give a small explanation. Also im not sure if I need to represent the vectors in A as columns or rows, or if either one works. For the next two problems, W is the subspace of R4 given by...
Problem No-3: The coordinates are shown in units of inches. Assume plane stress conditions. Let E 45x1 displacements have been determined to be u 1-0, v1 0.0025 in., u2 = 0.0012 in, v2 0.0001 in, u3 0, and v3 0.0025 in. Determine: (a) the stiffness matrix for the element shown [k] (b) the element stresses: ??, dy, and ? y and the principal stresses 06 psi, v = 0.25, and thickness t 1 in. The element nodal (15p) (20p) (0....
1. (10 points) Let T:P3 → P3 be the linear transformation satisfying T(x2 - 1) = x2 + x-3, T(2x) = 4x, and T(3x + 2) = 2(x + 3). Determine T(ax? + bx + c), where a, b, and c are arbitrary real numbers.
Problem #18: [2 marks] Let W be the subspace of R4 spanned by the vectors u - (1,0,1,0), u2 = (0.-1, 1.0), and ug = (0.0, 1,-1). Use the Gram-Schmidt process to transform the basis (uj, u, uz) into an orthonormal basi (A) v1 = (-12,0, 2.0), v2 - (VG VG VG, o), v3 - (I ) (B) v1 = (-V2.0, .), v2 - (VG VG VG o), v3 - (™J - V3 VI-V3) (C) v1 - ($2.0, 92.0), v2...
1. (10 points) Let T:P3 → P3 be the linear transformation satisfying T(x2 - 1) = x² + x - 3, T(2x) = 4x, and T(3x + 2) = 2(x + 3). Determine T(ax+ bx + c), where a, b, and c are arbitrary real numbers.
Problem 3 (10pt). Consider the sets V1 = {[a, b, c, d]T E R*: a+c=0}, V2 = {[a, b, c, d]T ER+ : a+c= 0,b+d=1}, V3 = {[a,b,c,d)' e R+ : ac =0}. Decide if V1, V2, V3 are subspaces of R4. Explain. Bonus (5pt). If one of V1, V2, V3 is a subspace find a basis for it and find its dimension.
5. Let T: P2(R) R3 be a linear transformation such that T(1) = (-1,2, -3), T(1 + 3x) = (4,-5,6), and T(1 + x²) = (-7,8,-9). a. Show that {1,1 + 3x ,1 + x2} is a basis for P(R) (7pts) b. Compute T(-1+ 4x + 2x²). (3pts)