Write a script (Program 2) to perform t he following matrix operations. Use output commands to clearly output each problem with a problem description and result.

(a) Create the following three matrices: A = [ 9 3 5 /2 4 2/ 6 10 5 ] B = [ 1 4 4/ 0 9 4/ 2 6 1 ] C = [ 8 15 1/ 10 8 2/ 8 5 10 ]

(b) Calculate A + B and B + A to show that addition of matrices is commutative.

(c) Calculate A +( B + C ) and ( A + B )+ C to show that addition of matrices is associative.

(d) Calculate 8( A + C ) and 8A + 8C to show that multiplication by a scalar is distributive.

(e) Calculate A( B + C ) and AB + AC to show that matrix multiplication is distributive.

(f) Does AB = BA ?

(g) Find AT (transpose of A ).

(h) Calculate B-1 (inverse of B ).

(i) Calculate the product BB-1 .

(j) Create a 2x2 matrix consisting of the lower left elements of B .

(k) Create a row vector that is the vector sum of the first row of A and the third row of C .

(l) Calculate the dot product of the second row of B and the third column of C