Mathematics II208010 marksNumerical: linear transformation computationIntroduction to linear transformations
Define Linear Transformation with an Example Let A = beginbmatrix 1 & -3 3 & 5 -1 & 7 endbmatrix, v = beginbmatrix -2 1 endbmatrix, b = beginbmatrix 3 2 1 endbmatrix, x = beginbmatrix x1 x2 endbmatrix, T(x) = Ax a. Find T(v) b. Find x in mathbbR2 whose image under T is b
Define Linear Transformation with an Example
Let $A = \begin{bmatrix} 1 & -3 \ 3 & 5 \ -1 & 7 \end{bmatrix}$, $v = \begin{bmatrix} -2 \ 1 \end{bmatrix}$, $b = \begin{bmatrix} 3 \ 2 \ 1 \end{bmatrix}$, $x = \begin{bmatrix} x_1 \ x_2 \end{bmatrix}$, $T(x) = Ax$
a. Find $T(v)$
b. Find $x \in \mathbb{R}^2$ whose image under $T$ is $b$ [10]
$$A = \begin{bmatrix} 1 & -3 \ 3 & 5 \ -1 & 7 \end{bmatrix}, \quad v = \begin{bmatrix} -2 \ 1 \end{bmatrix}, \quad b = \begin{bmatrix} 3 \ 2 \ 1 \end{bmatrix}, \quad x = \begin{bmatrix} x1 \ x2 \end{bmatrix}, \quad T(x) = Ax$$ --- A transformation $T: \mathbb{R}^n \to \mathbb{R}^m$ is a lin...