True or false every linear transformation is determined by a...

Name: true or false every linear transformation is determined by a matrix 24372
Uploaded: 2022-02-23T04:25:39-08:00
Duration: 2 min 27 s
Channel: Lakshya H
Description: true or false every linear transformation is determined by a matrix 24372

Mark each statement True or False. Justify each answer. a. A linear transformation is a special type of function. b. If $A$ is a $3 \times 5$ matrix and $T$ is a transformation defined by $T(\mathbf{x})=A \mathbf{x},$ then the domain of $T$ is $\mathbb{R}^{3}$. c. If $A$ is an $m \times n$ matrix, then the range of the transformation $\mathbf{x} \mapsto A \mathbf{x}$ is $\mathbb{R}^{m}$ . d. Every linear transformation is a matrix transformation. e. A transformation $T$ is linear if and only if $T\left(c_{1} \mathbf{v}_{1}+\right.$ $c_{2} \mathbf{v}_{2} )=c_{1} T\left(\mathbf{v}_{1}\right)+c_{2} T\left(\mathbf{v}_{2}\right)$ for all $\mathbf{v}_{1}$ and $\mathbf{v}_{2}$ in the domain of $T$ and for all scalars $c_{1}$ and $c_{2} .$