矩阵变换

Linear Transformations and Matrix Algebra

Introduction

Matrices as Functions

Transformations

Matrix Transformations

Let $A$ be a $3\times 2$ matrix and let $T(x)=Ax$ be the associated matrix transformation. Which statement is correct?

Let

and let $T(x)=Ax$. What is the range of $T$?

Let $A$ be an $m\times n$ matrix and let $T(x)=Ax$. The range of $T$ is the ______ of $A$. Enter two words.

Let

and let $T(x)=Ax$. Enter $T(u)$ for $u=(-1,-2,-3)$ as two numbers separated by commas (for example: 1,-2).

A chain of four masses joined by five springs is described by the $5\times 4$ matrix

whose transformation $T(u)=Au$ turns the displacements $u$ of the four masses into the extensions of the five springs. For $u=(2,5,1,3)$ enter $T(u)$ as five numbers separated by commas (for example: 1,2,3,4,5).

Let $A$ be an $m\times n$ matrix and let $T(x) = Ax$ be the associated matrix transformation. Which arrow describes $T$?

Let

and $x = (1,1)$. Compute $T(x) = Ax$ and enter the result as $x,y,z$.