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

Identify Matrix and Vector: Identify the matrix and the vector to be transformed. Matrix A = [[2,3],[-3,-1]] Vector v = [[4],[1]]Perform Matrix Multiplication: Perform matrix multiplication to find the image of the vector. Image of v, Av = [[2,3],[-3,-1]] * [[4],[1]] To multiply, take the dot product of the rows of A with the columns of v.Calculate First Element: Calculate the first element of the resulting vector. First element = (2 * 4) + (3 * 1) = 8 + 3 = 11Calculate Second Element: Calculate the second element of the resulting vector. Second element = (-3 * 4) + (-1 * 1) = -12 - 1 = -13Combine Results: Combine the results to get the image of the vector. The image of [[4],[1]] under the transformation is [[11],[-13]].

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Consider this matrix transformation:

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

Consider this matrix transformation: $\newline$ $\left[\begin{array}{cc} 2 & 3 \\ & \\ -3 & -1 \end{array}\right]$ $\newline$ What is the image of $\left[\begin{array}{l}4 \\ 1\end{array}\right]$ under this transformation?

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Q. Consider this matrix transformation:

\newline

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

\newline

What is the image of

\left[\begin{array}{l}4 \\ 1\end{array}\right]

under this transformation?

Identify Matrix and Vector: Identify the matrix and the vector to be transformed. Matrix $A = \left[\begin{array}{cc} 2 & 3 \ -3 & -1 \end{array}\right]$ Vector $v = \left[\begin{array}{c} 4 \ 1 \end{array}\right]$
Perform Matrix Multiplication: Perform matrix multiplication to find the image of the vector. $\newline$ Image of $v$ , Av = \begin{bmatrix}2 & 3\-3 & -1\end{bmatrix} * \begin{bmatrix}4\1\end{bmatrix} $\newline$ To multiply, take the dot product of the rows of $A$ with the columns of $v$ .
Calculate First Element: Calculate the first element of the resulting vector. $\newline$ First element = $(2 \times 4) + (3 \times 1) = 8 + 3 = 11$
Calculate Second Element: Calculate the second element of the resulting vector. $\newline$ Second element = $(-3 \times 4) + (-1 \times 1) = -12 - 1 = -13$
Combine Results: Combine the results to get the image of the vector. $\newline$ The image of \begin{bmatrix}4\1\end{bmatrix} under the transformation is \begin{bmatrix}11\-13\end{bmatrix}.