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

Get the answer to your homework problem.

Like

Report

Let $\mathcal{B}=\left\{\mathbf{b}_{1}, \mathbf{b}_{2}, \mathbf{b}_{3}\right\}$ be a basis for a vector space $V$ and $T : V \rightarrow \mathbb{R}^{2}$ be a linear transformation with the property that$$T\left(x_{1} \mathbf{b}_{1}+x_{2} \mathbf{b}_{2}+x_{3} \mathbf{b}_{3}\right)=\left[\begin{array}{c}{2 x_{1}-4 x_{2}+5 x_{3}} \\ {-x_{2}+3 x_{3}}\end{array}\right]$$Find the matrix for $T$ relative to $\mathcal{B}$ and the standard basis for $\mathbb{R}^{2} .$

$\left[\begin{array}{ccc}{2} & {-4} & {5} \\ {0} & {-1} & {3}\end{array}\right]$

Calculus 3

Chapter 5

Eigenvalues and Eigenvectors

Section 4

Eigenvectors and Linear Transformations

Vectors

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Lectures

02:56

In mathematics, a vector (…

06:36

01:23

Let $\mathcal{B}=\left\{\m…

06:21

Define $T : \mathbb{P}_{3}…

01:48

Let $\mathcal{D}=\left\{\m…

05:36

In $\mathbb{P}_{2},$ find …

08:39

Determine $T(\mathbf{v})$ …

Let $\left\{\mathbf{v}_{1}…

05:31

(a) Let $\mathbf{v}_{1}=(1…

02:06

Let $\mathbf{v}_{1}$ and $…

02:41

Let $\mathbf{p}_{1}(t)=1+t…

10:45

Find the change-of-basis m…

Okay, so for problem for I r. Again given assumption we have t of x one, be one of those x two you two plus x three The three It's the new vector, which is to x one minus four x two was five like three and ActiveX too. Plus three x three. So to find out the matrix for tea rented to be first need to find out the f B one from court in a C where C is Thea faces off off are too. So here we can just take X one to be one and next to x three to be zero. So our specter will be too zero. And similarly, we can find bee the F B two. So this will be negative for Nick to one and finally t f B three so T o b three Just be five and three now. So the Matrix TB, we'll just be the span off these three vectors. Two negative four and five zero negative one and three

View More Answers From This Book

Find Another Textbook

In mathematics, a vector (from the Latin word "vehere" meaning &qu…

In mathematics, a vector (from the Latin "mover") is a geometric o…

Let $\mathcal{B}=\left\{\mathbf{b}_{1}, \mathbf{b}_{2}, \mathbf{b}_{3}\right…

Define $T : \mathbb{P}_{3} \rightarrow \mathbb{R}^{4}$ by $T(\mathbf{p})=\le…

Let $\mathcal{D}=\left\{\mathbf{d}_{1}, \mathbf{d}_{2}\right\}$ and $\mathca…

In $\mathbb{P}_{2},$ find the change-of-coordinates matrix from the basis $\…

Determine $T(\mathbf{v})$ for the given linear transformation $T$ and vector…

Let $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}\right\}$ be a basis for the vecto…

(a) Let $\mathbf{v}_{1}=(1,1)$ and $\mathbf{v}_{2}=(1,-1) .$ Show that $\lef…

Let $\mathbf{v}_{1}$ and $\mathbf{v}_{2}$ be a basis for the vector space $V…

Let $\mathbf{p}_{1}(t)=1+t^{2}, \mathbf{p}_{2}(t)=t-3 t^{2}, \mathbf{p}_{3}(…

Find the change-of-basis matrix $P_{C \leftarrow B}$ from the given ordered …

05:52

In Exercises $25-28$ , show that the given signal is a solution of the diffe…

05:33

In Exercises 19 and 20, V is a vector space. Mark each statement True or Fal…

05:53

Construct a stage-matrix model for an animal species that has two life stage…

01:26

Exercises $7-12$ require MATLAB or other computational aid. In Exercises 7 a…

01:12

Use Exercise 27 to complete the proof of Theorem 1 for the case when $A$ is …

05:21

[M] Let $A$ be the matrix in Exercise $35 .$ Construct a matrix $C$ whose co…

Determine which sets of vectors are orthogonal.$\left[\begin{array}{r}{2…

01:54

In Exercises $9-16,$ find a basis for the eigenspace corresponding to each l…

03:01

In Exercises $9-18$ , construct the general solution of $\mathbf{x}^{\prime}…

02:48

Let $A$ be a real $n \times n$ matrix, and let $x$ be a vector in $\mathbb{C…

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.