The problem asks to compute the scalar multiplication of a matrix. We are given $M = \frac{1}{3} \begin{bmatrix} 1 & 0 \\ -6 & 5 \end{bmatrix}$. We need to find the matrix $M$.

1. Problem Description

The problem asks to compute the scalar multiplication of a matrix. We are given $M = \frac{1}{3} \begin{bmatrix} 1 & 0 \\ -6 & 5 \end{bmatrix}$. We need to find the matrix $M$.

2. Solution Steps

To find $M$, we need to multiply the scalar $\frac{1}{3}$ with each element of the matrix $\begin{bmatrix} 1 & 0 \\ -6 & 5 \end{bmatrix}$.

$M = \frac{1}{3} \begin{bmatrix} 1 & 0 \\ -6 & 5 \end{bmatrix} = \begin{bmatrix} \frac{1}{3}(1) & \frac{1}{3}(0) \\ \frac{1}{3}(-6) & \frac{1}{3}(5) \end{bmatrix}$

Now, we perform the scalar multiplication:

$\frac{1}{3}(1) = \frac{1}{3}$

$\frac{1}{3}(0) = 0$

$\frac{1}{3}(-6) = -2$

$\frac{1}{3}(5) = \frac{5}{3}$

So, $M = \begin{bmatrix} \frac{1}{3} & 0 \\ -2 & \frac{5}{3} \end{bmatrix}$.

3. Final Answer

$M = \begin{bmatrix} \frac{1}{3} & 0 \\ -2 & \frac{5}{3} \end{bmatrix}$