Question

If $A = \begin{bmatrix} \frac{2}{3} & 1 & \frac 53 \\\[0.3em] \frac{1}{3} & \frac 23 & \frac{4}{3} \\\[0.3em] \frac 73 & 2 & \frac{2}{3} \end{bmatrix}$ and $B = \begin{bmatrix} \frac{2}{5} & \frac 35 & 1 \\\[0.3em] \frac{1}{5} & \frac 25 & \frac{4}{5} \\\[0.3em] \frac 75 & \frac 65 & \frac{2}{5} \end{bmatrix}$ then compute 3A-5B.

Answer 1

3A - 5B = 3$\begin{bmatrix} \frac{2}{3} & 1 & \frac 53 \\\[0.3em] \frac{1}{3} & \frac 23 & \frac{4}{3} \\\[0.3em] \frac 73 & 2 & \frac{2}{3} \end{bmatrix}$- 5 $\begin{bmatrix} \frac{2}{5} & \frac 35 & 1 \\\[0.3em] \frac{1}{5} & \frac 25 & \frac{4}{5} \\\[0.3em] \frac 75 & \frac 65 & \frac{2}{5} \end{bmatrix}$

          = $\begin{bmatrix}        2 & 3 & 5           \\\[0.3em]        1 & 2           & 4 \\\[0.3em]       7          & 6 & 2    \end{bmatrix}$- $\begin{bmatrix}        2 & 3 & 5           \\\[0.3em]        1 & 2           & 4 \\\[0.3em]       7          & 6 & 2    \end{bmatrix}$

          = $\begin{bmatrix}        0 & 0 & 0           \\\[0.3em]        0 & 0           & 0 \\\[0.3em]       0          & 0 & 0    \end{bmatrix}$