Chapter 1

Question#1: Which of the following are conformable for addition? Solution: \[\begin{align}& A=\left[ \begin{matrix}   2 & 1  \\   -1 & 3  \\\end{matrix} \right],B=\left[ \begin{matrix}   3  \\   1  \\\end{matrix} \right],C=\left[ \begin{matrix}   1 & 0  \\   2 & -1  \\   1 & -2  \\\end{matrix} \right] \\ & D=\left[ \begin{matrix}   2+1  \\   3  \\\end{matrix} \right],E=\left[ \begin{matrix}   -1 & 0  \\   … Read more

Question#1: Which of the following product of matrices is conformable for multiplications? \(i\) \[\left[ \begin{matrix}  1 & -1  \\   0 & 2  \\\end{matrix} \right]\left[ \begin{matrix}   -2  \\   3  \\\end{matrix} \right]\] Solution: \[\begin{align}\left[ \begin{matrix}  1 & -1  \\   0 & 2  \\\end{matrix} \right]\left[ \begin{matrix}   -2  \\   3  \\\end{matrix} \right]\\\text{Order of first Matrix}&=2-by-\bbox[5px, border: 1px solid red]{2} … Read more

Question#1: Find the determinant of the following matrices. \(i\) \[A=\left[ \begin{matrix}   -1 & 1  \\   2 & 0  \\\end{matrix} \right]\] Solution: \[\begin{align}  \left| A \right|&=\left| \begin{matrix}   -1 & 1  \\   2 & 0  \\\end{matrix} \right| \\ & =\left( -1 \right)\left( 0 \right)-\left(1 \right)\left( 2 \right) \\ & =0-2 \\ & =-2 \\  \end{align}\] \(ii\) \[B=\left[ \begin{matrix}   1 & 3  … Read more