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

Consider this matrix transformation:\newline[2−113] \left[\begin{array}{cc} 2 & -1 \\ 1 & 3 \end{array}\right] \newlineWhat is the image of [23] \left[\begin{array}{l}2 \\ 3\end{array}\right] under this transformation?

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Q. Consider this matrix transformation:\newline[2−113] \left[\begin{array}{cc} 2 & -1 \\ 1 & 3 \end{array}\right] \newlineWhat is the image of [23] \left[\begin{array}{l}2 \\ 3\end{array}\right] under this transformation?
  1. Write Matrix Transformation: Write down the matrix transformation and the vector to be transformed.\newlineMatrix transformation: [2−1 13]\begin{bmatrix} 2 & -1 \ 1 & 3 \end{bmatrix}\newlineVector: [2 3]\begin{bmatrix} 2 \ 3 \end{bmatrix}
  2. Perform Matrix Multiplication: Perform matrix multiplication to find the image of the vector under the transformation.\newlineTo multiply the 2×22 \times 2 matrix by the 2×12 \times 1 vector, we take the dot product of the rows of the matrix with the columns of the vector.\newlineFirst row of the matrix times the vector: (2×2)+(−1×3)=4−3=1(2 \times 2) + (-1 \times 3) = 4 - 3 = 1\newlineSecond row of the matrix times the vector: (1×2)+(3×3)=2+9=11(1 \times 2) + (3 \times 3) = 2 + 9 = 11
  3. Write Resulting Vector: Write down the resulting vector, which is the image of the original vector under the transformation.\newlineThe resulting vector (image) is: \left[\begin{array}{c}1\11\end{array}\right]

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