Consider the linear transformation

Lennie Carroll
2020-10-20
Answered

Consider the linear transformation

You can still ask an expert for help

irwchh

Answered 2020-10-21
Author has **102** answers

asked 2021-09-16

Let A be an

Show that:

a)

b)

asked 2021-03-02

Use $AB\leftarrow \to$ and $CD\leftarrow \to$ to answer the question. $AB\leftarrow \to$ contains the points A(2,1) and B(3,4). $CD\leftarrow \to$ contains the points C(−2,−1) and D(1,−2). Is $AB\leftarrow \to$ perpendicular to $CD\leftarrow \to$ ? Why or why not?

asked 2021-09-20

The reduced row echelon form of the augmented matrix of a system of linear equations is given. Determine whether this system of linear equations is consistent and, if so, find its general solution.

Write the solution in vector form.

asked 2022-02-01

Find the matrix representation of the linear transformation T that maps the input vector $\overrightarrow{x}}_{1}={(1,1)}^{T$ to the output vector $\overrightarrow{y}}_{1}={(2,-3)}^{T$ and maps the input vector $\overrightarrow{x}}_{2}={(1,2)}^{T$ to the output vector $\overrightarrow{y}}_{2}={(5,1)}^{T$

asked 2021-12-03

Explain why the columns of an n x n matrix A are linearly independent when A is invertible.

asked 2022-05-26

Let $T$ be the transformation of 2 by 2 real symmetric matrices defined by:

$\left[\begin{array}{cc}a& b\\ b& c\end{array}\right]$

$\left[\begin{array}{cc}c& -b\\ -b& a\end{array}\right]$

then which of the following statements is NOT true?

1. $det(T)=-1$

2. ${T}^{-1}=T$

3. $T$ is linear

4. the space of 2 by 2 real symmetric matricies with only zeros in the main diagonal is an eigenspace of $T$.

5. $\lambda =2$ is an eigen value of $T$

$\left[\begin{array}{cc}a& b\\ b& c\end{array}\right]$

$\left[\begin{array}{cc}c& -b\\ -b& a\end{array}\right]$

then which of the following statements is NOT true?

1. $det(T)=-1$

2. ${T}^{-1}=T$

3. $T$ is linear

4. the space of 2 by 2 real symmetric matricies with only zeros in the main diagonal is an eigenspace of $T$.

5. $\lambda =2$ is an eigen value of $T$

asked 2022-05-21

Define a matrix transformation A as follows:

A = {{1, -1}, {2, -2}, {3, -3}};

Find the image of {1,3} under A and determine if {3,6,9} is in the range of the transformation.

A = {{1, -1}, {2, -2}, {3, -3}};

Find the image of {1,3} under A and determine if {3,6,9} is in the range of the transformation.