Question

dilate the given triangle by a magnitude of 3.
\\( \

$$\begin{bmatrix} 3 & 6 & 3 \\\\ -3 & 3 & 3 \\end{bmatrix}$$

\\)
\\( \

$$\begin{bmatrix} 9 & ? & \\\\ -9 & & \\end{bmatrix}$$

\\)

Explanation:

Step1: Understand dilation rule

Dilation by a magnitude \(k = 3\) means multiply each element of the original matrix by \(3\).

Step2: Calculate the first unknown (top - middle)

Original top - middle element is \(6\). Multiply by \(3\): \(6\times3=18\).

Step3: Calculate the bottom - middle

Original bottom - middle element is \(3\). Multiply by \(3\): \(3\times3 = 9\).

Step4: Calculate the top - right

Original top - right element is \(3\). Multiply by \(3\): \(3\times3=9\).

Step5: Calculate the bottom - right

Original bottom - right element is \(3\). Multiply by \(3\): \(3\times3 = 9\).

Answer:

The completed matrix is \(

$$\begin{bmatrix}9&18&9\\-9&9&9\end{bmatrix}$$

\). So the green box (top - middle) is \(18\), the bottom - middle is \(9\), the top - right is \(9\), and the bottom - right is \(9\).