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

Consider this matrix transformation:\newline[−32232−1−32−3] \left[\begin{array}{ccc} -3 & 2 & 2 \\ 3 & 2 & -1 \\ -3 & 2 & -3 \end{array}\right] \newlineWhat is the image of [5−42] \left[\begin{array}{c}5 \\ -4 \\ 2\end{array}\right] under this transformation?

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Q. Consider this matrix transformation:\newline[−32232−1−32−3] \left[\begin{array}{ccc} -3 & 2 & 2 \\ 3 & 2 & -1 \\ -3 & 2 & -3 \end{array}\right] \newlineWhat is the image of [5−42] \left[\begin{array}{c}5 \\ -4 \\ 2\end{array}\right] under this transformation?
  1. Write Matrix and Vector: Write down the matrix and the vector to be transformed.\newlineMatrix: [−322 32−1 −32−3]\begin{bmatrix}-3 & 2 & 2 \ 3 & 2 & -1 \ -3 & 2 & -3\end{bmatrix}\newlineVector: [5 −4 2]\begin{bmatrix}5 \ -4 \ 2\end{bmatrix}
  2. Perform Matrix Multiplication: Perform matrix multiplication to find the image of the vector.\newlineTo multiply the matrix by the vector, we take the dot product of each row of the matrix with the vector.\newlineFirst row: (−3×5)+(2×−4)+(2×2)=−15−8+4=−19(-3 \times 5) + (2 \times -4) + (2 \times 2) = -15 - 8 + 4 = -19\newlineSecond row: (3×5)+(2×−4)+(−1×2)=15−8−2=5(3 \times 5) + (2 \times -4) + (-1 \times 2) = 15 - 8 - 2 = 5\newlineThird row: (−3×5)+(2×−4)+(−3×2)=−15−8−6=−29(-3 \times 5) + (2 \times -4) + (-3 \times 2) = -15 - 8 - 6 = -29
  3. Write Resulting Image Vector: Write down the resulting image vector.\newlineThe 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]

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