Linear Algebra Questions

Solve the following problems (and show work). 1. Consider the two bases B = {(1,0,1), (1,1,2), (0,2,3)} and B' = {(2,3,1), (1,2,0), (2,0,3)} of R3. a. Find the change of basis matrix from B to B'. b. Find the change of basis matrix from B' to B. c. Given the vector v = (2, 2, 1), first find the coordinate vector (12),; via row reduction and then compute the coordinate vector(v)3r using one of your change- ofbasis matrices. Consider the standard basis B = {31, 32, 93} of R3 and an alternate basis 3' = {(1,3, 2), (1, 4,3), (2, 4,3)}. a. Determine the change-ofbasis matrices PB>B' and PB'>B- b. Use one of your matrices to show how to express the vector (3, 1,2) in terms of its B'-coordinates. Given the linear transformation T(x1,x2,x3,x4) = (x1 + 296; x4, x1 2x2, 3x1 + x3 + 3x4, x2 x3, x1 x4). a. What is the domain of T? b. What is the codomain of T? c. Determine T(0, 1,4-,1). d. Find the standard matrix for T