Solutions to Assignment 1

1. B^{−1}A^{−1}Z^{−1}Y^{−1}X^{−1}.

2. Not Invertible as in the Echelon Formthere is a row of all Zeros.

3. R2^{′} = R_{2} + \frac{1}{2}R_{1}.

4. (ad − bc) ≠ 0. While reducing the given Matrix [ \begin{matrix}a & b \\ c & d \end{matrix} ] into Reduced Echelon form, that means to I_{2} = [ \begin{matrix}1 & 0 \\ 0 & 1 \end{matrix} ], one of the row operation is, to divide a row by (ad − bc). Hence we require (ad − bc) term to be non zero.