7. Let C=[²4] D=[²₁ Find i. ii. iii. iv. 2 1 0 0 1 C' D' CD (CD)'

Use an example chosen from 22 matrices to show that for nn matrices A and B,ABBA but AB=BA.

Find the sequence of the elementary matrices whose product is the non singular matrix below. [2410]

Show that |a1111a1111a1111a|=(a+3)(a1)3

Consider the matrix A=[2314]. Show that any of the three types of elementary row operations can be used to create a leading 1 at the top of the first column. Which do you prefer and why?

15. Reverse the elementary row operations used in Example 2.9 to show that we can convert

Use elementary matrices to find the inverse of A=1a0010001100b1000110001000c, c0.

Can you explain whether a 2×2 matrix with an entire row of zeros can have an inverse?

Explain what is meant by the minor of an entry in a square matrix.

Solve for x,y and z in the matrix equation 4xyz-1=2yz-x1+24x5-x.