(a) T/ F? if. n is an even positive integer. then the product of all eigenvalues (counting with multiplicities) is equal to det(A). (b) Without assuming it is even. compute the product of all eigenvalues (counting with multiplicities). Your answer should be written in terms of A. G'EECU-i'g Cite-orig _ __ 024: Let X and Y be n x n matrices such that PY = XP for some n x n invertible matrix P. Let v_i. .. in this order, and let B be the ordered basis of R'n given by v_1. ..., v_n. ., v_n be the columns of P T/ F? Y; [XLB (i.e., Y is the n x n matrix representation of X with respect to the basis B). 025: T/ F? Two n x n matrices are similar if and only if they represent the same linear map from R'n to R'n (with respect .. to possibly different bases). 026: Let v be the vector given by the following 2 x1 matrix: \"I 2 (a) Compute the orthogonal projection of v with respectto the line spanned by e_1. (b) Compute the orthogonal projection of v with respect to the line spanned by e_2. (c) Compute the orthogonal proiection of v with respect to the line spanned by e_'l + e_2. (d) Compute the orthogonal proiection of v with respect to the line spanned by e_1 - e_2