Consider this matrix transformation: [[-3,2,2],[3,2,-1],[-3,2,-3]] What is the image of this transformation? [[5],[-4],[2]] under

Write Matrix and Vector: Write down the matrix and the vector to be transformed. Matrix: [[-3,2,2],[3,2,-1],[-3,2,-3]] Vector: [[5],[-4],[2]]Perform Matrix Multiplication: Perform matrix multiplication to find the image of the vector. To multiply the matrix by the vector, we take the dot product of each row of the matrix with the vector. First row: (-3 * 5) + (2 * -4) + (2 * 2) = -15 - 8 + 4 = -19 Second row: (3 * 5) + (2 * -4) + (-1 * 2) = 15 - 8 - 2 = 5 Third row: (-3 * 5) + (2 * -4) + (-3 * 2) = -15 - 8 - 6 = -29Write Resulting Image Vector: Write down the resulting image vector. The image of the vector [[5],[-4],[2]] under the given matrix transformation is: [[-19],[5],[-29]]

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Q. Consider this matrix transformation:

\newline

\left[\begin{array}{ccc} -3 & 2 & 2 \\ 3 & 2 & -1 \\ -3 & 2 & -3 \end{array}\right]

\newline

What is the image of

\left[\begin{array}{c}5 \\ -4 \\ 2\end{array}\right]

under this transformation?

Write Matrix and Vector: Write down the matrix and the vector to be transformed. $\newline$ Matrix: $\begin{bmatrix}-3 & 2 & 2 \ 3 & 2 & -1 \ -3 & 2 & -3\end{bmatrix}$ $\newline$ Vector: $\begin{bmatrix}5 \ -4 \ 2\end{bmatrix}$
Perform Matrix Multiplication: Perform matrix multiplication to find the image of the vector. $\newline$ To multiply the matrix by the vector, we take the dot product of each row of the matrix with the vector. $\newline$ First row: $(-3 \times 5) + (2 \times -4) + (2 \times 2) = -15 - 8 + 4 = -19$ $\newline$ Second row: $(3 \times 5) + (2 \times -4) + (-1 \times 2) = 15 - 8 - 2 = 5$ $\newline$ Third row: $(-3 \times 5) + (2 \times -4) + (-3 \times 2) = -15 - 8 - 6 = -29$
Write Resulting Image Vector: Write down the resulting image vector. $\newline$ The image of the vector \left[\begin{array}{c}5\-4\2\end{array}\right] under the given matrix transformation is: $\newline$ \left[\begin{array}{c}-19\5\-29\end{array}\right]