1. Simplify each of the following expressions when possible. If the addition or multiplication cannotbe done explain why. (Note: You must give the order of the matrix as part of your explanation.)(a) A + D(b) A + E(c) B + D(d) A × B(e) B × A1(f) C × A(g) 12D(h) C − 12D

4. What should be added to (3x 4) to get (9x - 7)? a)( 12 x? - 11) b) (12 x 11) c)(6x? - 11) d) (6x² 11)​

9.Question 9Matrix multiplication works if its two operands1 pointare vectors; specifically, the first one is a column vector and the second one is a row vector of any length.are scalars. are square matrices of the same size.The first and second options are correct.The second and third options are correct.All of the options are correct.

solve the matrix chain multiplication problem and achieve the optimal parenthesization.

A sequence of elementary row operations transforms the matrix [a b c d e f ] to the matrix[d+2a e+2b f+2c a b c ]Which one of the following sequences could have this effect?1.First R1↦R1+2R2; then R1↔R2.2.First R1↔R2; then R1↦R1−2R23.First R1↦R2+2R1; then R1↔R2.4.First R1↦2R1; thenR1↔R2.

2. Consider the following matrices.[ 1 3−2 6](a)[1 −91 −5](b)1 2 0−1 −1 10 1 1(c)1 1 00 −2 10 0 3(d)1 1 01 0 10 1 1(e)1 1 −10 2 0−1 1 1(f)4 0 12 3 2−1 0 2(g)1 0 32 −2 23 0 1(h)3 1 0 0−1 1 0 00 0 1 40 0 1 1(i)2 1 1 10 1 2 30 0 3 30 0 0 2(j)1 0 0 00 1 0 01 1 3 0−2 1 2 −1(k)1 1 1 04 1 0 10 0 −1 10 0 2 0(l)For each of the matrix, find(i) the characteristic polynomial