Question

each column of the matrix ( t=left\begin{array}{lll}0 & 0 & 3 \\ 0 & 3 & 0end{array}
ight ) represents a vertex of a triangle. if rosa scales the triangle by finding ( 3 t ), what are the vertices of the scaled triangle?
( (3,3),(3,9),(9,3) )
( (0,0),(0,6),(6,0) )
( (3,3),(0,9),(9,0) )
( (0,0),(0,9),(9,0) )

Explanation:

Step1: Multiply the matrix by the scalar

When scaling a matrix \(T=

$$\begin{bmatrix}0&0&3\\0&3&0\end{bmatrix}$$

\) by a scalar \(3\), we use the rule for scalar - matrix multiplication. If \(A = [a_{ij}]\) is an \(m\times n\) matrix and \(k\) is a scalar, then \(kA=[ka_{ij}]\).

For the first column \(

$$\begin{bmatrix}0\\0\end{bmatrix}$$

\), when multiplied by \(3\) we get \(3\times

$$\begin{bmatrix}0\\0\end{bmatrix}$$

=

$$\begin{bmatrix}3\times0\\3\times0\end{bmatrix}$$

=

$$\begin{bmatrix}0\\0\end{bmatrix}$$

\)

For the second column \(

$$\begin{bmatrix}0\\3\end{bmatrix}$$

\), when multiplied by \(3\) we get \(3\times

$$\begin{bmatrix}0\\3\end{bmatrix}$$

=

$$\begin{bmatrix}3\times0\\3\times3\end{bmatrix}$$

=

$$\begin{bmatrix}0\\9\end{bmatrix}$$

\)

For the third column \(

$$\begin{bmatrix}3\\0\end{bmatrix}$$

\), when multiplied by \(3\) we get \(3\times

$$\begin{bmatrix}3\\0\end{bmatrix}$$

=

$$\begin{bmatrix}3\times3\\3\times0\end{bmatrix}$$

=

$$\begin{bmatrix}9\\0\end{bmatrix}$$

\)

Answer:

C. \((3,0),(0,9),(9,0)\)