each column of the matrix $t = \\begin{bmatrix}0&0&3\\\\0&3&0\\end{bmatrix}$ represents a vertex of a…

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

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

Answer

Explanation:

Step1: Recall scalar - matrix multiplication rule

To find (3T), multiply each element of matrix (T=\begin{bmatrix}0&0&3\0&3&0\end{bmatrix}) by 3.

Step2: Calculate the first - column elements of (3T)

(3\times0 = 0), (3\times0=0).

Step3: Calculate the second - column elements of (3T)

(3\times0 = 0), (3\times3 = 9).

Step4: Calculate the third - column elements of (3T)

(3\times3=9), (3\times0 = 0).

Step5: Write the vertices

The vertices of the scaled triangle are ((0,0)), ((0,9)), ((9,0)) from the columns of (3T=\begin{bmatrix}0&0&9\0&9&0\end{bmatrix}).

Answer:

D. ((0,0),(0,9),(9,0))