### Home > PC3 > Chapter 9 > Lesson 9.1.3 > Problem9-54

9-54.

Perform each of the following matrix operations without using a calculator. If the operation is impossible, explain why.

 $\begin{bmatrix} {1} & { -4 } & { 0} \\ { -2 } & { 5 } & { 3 } \end{bmatrix}$ $\begin{bmatrix} {-1} & { 0 } \\ { 2 } & { 4 } \\ { -5 } & { -3 }\end{bmatrix}$ $=\begin{bmatrix} {1(-1)+(-4)(2)+0(-5)} & { 1(0)+(-4)(4)+0(-3) } \\ { (-2)(-1)+5(2)+3(-5) } & { (-2)(0)+5(4)+3(-3) } \end{bmatrix}$ $=\begin{bmatrix} {-9} & { -16 } \\ { -3 } & { 11 } \end{bmatrix}$ $2 \times 3$ $3 \times 2$ $2 \times 2$

1. $\left[ \begin{array} { l l l } { 4 } & { 9 } & { 2 } \\ { 6 } & { 0 } & { 5 } \end{array} \right] \left[ \begin{array} { l } { a } \\ { b } \\ { c } \end{array} \right]$

Multiplying a $2 \times 3$ matrix by a $3 \times 1$ matrix results in a $2 \times 1$ matrix.

1. $2 \left[ \begin{array} { r r r } { 4 } & { 9 } & { 2 } \\ { 6 } & { 0 } & { - 5 } \end{array} \right] + \left[ \begin{array} { r r r } { 1 } & { 0 } & { - 3 } \\ { 0 } & { 4 } & { 1 } \end{array} \right]$

$\begin{bmatrix}8&18&4\\12&0&-10\end{bmatrix}+\begin{bmatrix}1&0&-3\\0&4&1\end{bmatrix}$

1. $\left[ \begin{array} { l l } { a } & { b } \\ { c } & { d } \end{array} \right] \left[ \begin{array} { l l } { e } & { f } \end{array} \right]$

Is it possible to multiply a $2 \times 2$ matrix by a $1 \times 2$ matrix?

1. $\left[ \begin{array} { l l } { a } & { b } \\ { c } & { d } \end{array} \right] + \left[ \begin{array} { l l } { e } & { f } \end{array} \right]$

Is it possible to add two matrices with different dimensions?

1.  $\begin{vmatrix} 10 & 1 \\ -9 & 2 \\ \notag \end{vmatrix}$

$\begin{vmatrix} a & b \\ c & d \\ \notag \end{vmatrix} = ad-cb$

1.  $\begin{vmatrix} 4 & 2 & 5 \\ 10 & 3 & -6 \\ \notag \end{vmatrix}$

See the hint in part (e). Is this a square matrix?