Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Let $\mathbf{x}=\left[\begin{array}{c}{x_{1}} \\ {x_{2}}\end{array}\right], \mathbf{v}_{1}=\left[\begin{array}{r}{-2} \\ {5}\end{array}\right],$ and $\mathbf{v}_{2}=\left[\begin{array}{r}{7} \\ {-3}\end{array}\right],$ and let $T : \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ be a linear transformation that maps $\mathbf{x}$ into $x_{1} \mathbf{v}_{1}+x_{2} \mathbf{v}_{2} .$ Find a matrix $A$ such that $T(\mathbf{x})$ is $A \mathbf{x}$ for each $\mathbf{x}$.

See Solution

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 8

Introduction to Linear Transformations

Introduction to Matrices

Campbell University

McMaster University

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

02:41

Let $T_{1}: \mathbb{R}^{2}…

02:18

In Exercises $17-20,$ show…

03:41

Assume that $T$ defines a …

01:23

Determine the matrix of th…

02:39

03:45

02:28

For Problems $14-18$, dete…

01:48

01:15

Determine the linear trans…

03:37

Let $T : \mathbb{R}^{2} \r…

eso were given a vector X view one and three to and we have a defined, uh, function t of x where X is a vector is equal Thio x one be one plus x to be to go where X is just the vector x one next to V one is you quarter negative to five and he too is equal to seven Negative three. So it's really write this in matrix for so Tia Vex can be written as the vectors If you want be too Times X one extra right, cause thes air columns So this is a two by two matrix and this is our vector X, which has the following. Uh, he's underlined components so we can rewrite to you Vex like this. And so now let's Ah plugin RV wannabe too. The one was minus 25 He, too was seven minus three. Then we have x one x two. So, um, we've done everything to answer the question. So if we call this matrix A, we found a matrix. A such that t of X is equal to a X, So the system matrix we need

View More Answers From This Book

Find Another Textbook

Numerade Educator

In mathematics, the absolute value or modulus |x| of a real number x is its …

Let $T_{1}: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ and $T_{2}: \mathbb{R…

In Exercises $17-20,$ show that $T$ is a linear transformation by finding a …

Assume that $T$ defines a linear transformation and use the given informatio…

Determine the matrix of the given transformation $$T: \mathbb{R}^{2} \righta…

For Problems $14-18$, determine the matrix of the given transformation$$…

Determine the linear transformation $T: \mathbb{R}^{n} \rightarrow \mathbb{R…

Let $T : \mathbb{R}^{2} \rightarrow \mathbb{R}^{3}$ be a linear transformati…

01:44

Suppose $P$ is invertible and $A=P B P^{-1} .$ Solve for $B$ in terms of $A …

In Exercises $5-8,$ use the definition of $A \mathbf{x}$ to write the matrix…

04:08

In Exercises $7-12$ , describe all solutions of $A \mathbf{x}=0$ in parametr…

04:27

Row reduce the matrices in Exercises 3 and 4 to reduced echelon form. Circle…

01:14

Simplify each expression. Write all answers with only positive exponents. As…

08:36

USING STRUCTURE ind the circumference of each circle.a. a circle circums…

03:06

In Exercises $5-8,$ determine if the columns of the matrix form a linearly i…

04:26

Prove Theorem 2$(\mathrm{b})$ and 2$(\mathrm{c}) .$ Use the row-column rule.…

00:26

In Exercises $19-22,$ convert the angle measure.(See Example. 5.)Con…

01:20

Suppose $A$ and $B$ are $n \times n, B$ is invertible, and $A B$ is invertib…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.