Question

Find the matrix $A$ of the linear transformation from $\mathbb{R}^2$ to $\mathbb{R}^3$ given by $\begin{bmatrix} x_1\\x_2 \end{bmatrix} = \begin{bmatrix} 9\\7\\-5 \end{bmatrix} x_1 + \begin{bmatrix} -2\\-9\\-6 \end{bmatrix} x_2.$

          Find the matrix $A$ of the linear transformation from $\mathbb{R}^2$ to $\mathbb{R}^3$ given by
$\begin{bmatrix} x_1\\x_2 \end{bmatrix} = \begin{bmatrix} 9\\7\\-5 \end{bmatrix} x_1 + \begin{bmatrix} -2\\-9\\-6 \end{bmatrix} x_2.$

Find the matrix A of the linear transformation from ℝ^2 to ℝ^3 given by
< b m a t r i x >
=
< b m a t r i x >
x1 +
< b m a t r i x >
x2.

Added by Katie D.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Supreeta N

02/23/2023

Step 1

Step 1: The matrix $A$ is the matrix whose columns are the images of the standard basis vectors under the transformation $T$. Show more…

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Find the matrix $A$ of the linear transformation from $\mathbb{R}^2$ to $\mathbb{R}^3$ given by $T \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = \begin{bmatrix} 9 \\ 7 \\ -5 \end{bmatrix} x_1 + \begin{bmatrix} -2 \\ -9 \\ -6 \end{bmatrix} x_2$. $A = \begin{bmatrix} \Box & \Box \\ \Box & \Box \\ \Box & \Box \end{bmatrix}$.