Question

Let $x = \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}$, $v_1 = \begin{bmatrix} -3 \\ 6 \end{bmatrix}$, and $v_2 = \begin{bmatrix} -9 \\ 2 \end{bmatrix}$ and let $T: \mathbb{R}^2 \to \mathbb{R}^2$ be a linear transformation that maps $x$ into $x_1v_1 + x_2v_2$. Find a matrix $A$ such that $T(x)$ is $Ax$ for each $x$. $A = \begin{bmatrix} 3 & -9 \\ 6 & 2 \end{bmatrix}$

          Let $x = \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}$, $v_1 = \begin{bmatrix} -3 \\ 6 \end{bmatrix}$, and $v_2 = \begin{bmatrix} -9 \\ 2 \end{bmatrix}$ and let $T: \mathbb{R}^2 \to \mathbb{R}^2$ be a linear transformation that maps $x$ into $x_1v_1 + x_2v_2$. Find a matrix $A$ such that $T(x)$ is $Ax$ for each $x$.
$A = \begin{bmatrix} 3 & -9 \\ 6 & 2 \end{bmatrix}$

Let x =
< b m a t r i x >, v1 =
< b m a t r i x >, and v2 =
< b m a t r i x > and let T: ℝ^2 →ℝ^2 be a linear transformation that maps x into x1v1 + x2v2. Find a matrix A such that T(x) is Ax for each x.
A =
< b m a t r i x >

Added by Pablo S.

Elementary and Intermediate Algebra

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

Instant Answer

Solved by Expert Ashley Boni

08/07/2019

Step 1

Step 1: Understand the problem The problem is asking to find a matrix A such that the linear transformation T maps x into x_(1)v_(1) + x_(2)v_(2), and this mapping can be represented by the matrix multiplication Ax for each x in R^(2). Show more…

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The provided text contains several errors, including spelling, typographical, and formatting issues. Here is the corrected version: Let x = [[x_(1)], [x_(2)]], v_(1) = [[-3], [6]], and v_(2) = [[-9], [2]], and let T: R^(2) -> R^(2) be a linear transformation that maps x into x_(1)v_(1) + x_(2)v_(2). Find a matrix A such that T(x) = Ax for each x. A = [[3, -9], [6, 2]] The text "F93.0 Letx= andva and let TR2R2 be a linear transformation that maps into V+XV.Find a matrix Asuch that T(x is Ax for each x" appears to be incomplete and contains errors. It is unclear what the intended meaning is, and without a complete and coherent sentence, it is not possible to correct the errors accurately. Please provide the complete text for further assistance.