Let U be a square matrix such that u'U=I. Show that det U = +1. Assume that U'u=1. Since the desired result is that det U= +1, an intermediate step must be found which contains the expression det U. Which of the following can be applied to the assumption U'U=I to achieve the desired resulr? OA. det (U'u)-1= det I OB. det (UTu) =1 OC. det (UTu)=det 1 O D. (UTU)-1=1-1 Simplify the right side of the equation found in the first step. Which property can be used to simplify the left side of the equation found in the first step? Select all that apply. OA. det U = - det U OB. UTU=1 OC. Multiplicative Property O D. Commutative Property DE. det U= det U Use the properties from the previous step to rewrite the left side of the equation found in the first step. (2 Setting each side of the equation in the first step equal to the expressions found in previous steps and solving for det U results in det U=1. Click to select your answer(s).

5. Find the orthogonal projection of b = (1,-1,2) onto the left null space of the matrix A = -6

Hlo expert don't Use chat gpt plz  Let A be a 4 × 4 matrix with row vectors a,b, c, and d. Assume that det(A) = 7. 1.Find the determinant of matrix B with rows 3b, a, c− 2b,d. 2.Pick any non-zero matrix A that satisfies the condition above, find the corresponding B and the Minkowski product its first two row vectors. 3.Find the Euclidean norm of the first row vector of B. 4.Illustrate the Cauchy-Schwarz inequality for the first two row vectors of B.

9. Given the bases B = {1+2t, 2+t} and C = {1-t, 2-3t} of P₁. Find the change of coordinates matrix Pc-B from B to C.

Only (a) and (d) and (e).

Please show all steps clearly, thank you.