Which of the following matrices are invertible? (Select all of them.) 0 0 (88). (13). (8 5). The 3 x 3 identity matrix. The 2 x 2 matrix corresponding to counterclockwise rotation by π/3.

Let A be a 2 x 2 matrix If ad – bc + 0, then -1 A. such that [1 AA-1 = A-'A Let -1] 3. (a) Find A-1. (b) Find A?. (c) Find (A-1)?. (d) Show that (A-1)² is the inverse of A?.

5. (16 points) Let A = [²3¹], B = [−1¹ 63], and C = [29]. Compute each matrix sum or product if it is defined. If an expression is undefined, explain why. (a) 2A + 3C (b) C-B (c) AB (d) BA

Linear Algebra

Consider the Matrix

102 -1 -2 For A = [0 2 -2] find Q that diagonalizes this symmetric matrix. 0

Find a matrix P such that P'AP orthogonally diagonalizes A. Verify that P'AP gives the proper diagonal form. (Enter each matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list.) -6 12 A = 6 -12 12 -12 (Р, РТАР) %3 Need Help? Read It

04 * Consider two invertible matrices A and B. Which one of the following is equal to A(AB)-¹B? AB^-1AB ABA^-1B AB^-1A^-1B AB^-1B^-1A

Г1 2 1 A = 3 1 -2 0 1 Let Find the cofactor matrix C and the inverse matrix A!.