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Consider the vectors $\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3},$ and $\mathbf{b}$ in $\mathbb{R}^{2},$ shown in the figure. Does the equation $x_{1} \mathbf{v}_{1}+x_{2} \mathbf{v}_{2}+x_{3} \mathbf{v}_{3}=\mathbf{b}$ have a solution? Is the solution unique? Use the figure to explain your answers.figure can't copy

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Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 3

Vector Equations

Introduction to Matrices

Oregon State University

McMaster University

Harvey Mudd College

Lectures

01:32

In mathematics, the absolu…

01:11

05:08

Copy the vectors in the fi…

04:28

02:11

01:23

(FIGURE CAN'T COPY)

0:00

07:31

00:58

For the following exercise…

01:22

00:45

Find the vectors $\mathbf{…

Okay, so for a problem 32 we consider four vectors, you won't be one B two, B three and B in, uh are to space. So I'll just draw this briefly. Be one and I mean to and the three. And this is our baby now, too, to figure out whether whether whether x one has we won us expert I'm svp plus fax three times +33 It was be as has a solution or not. It is, Actually, we need to consider the system First matrix spend by if you want me to be three be too the three times the times unknown, Victor X Salon X two and next three, which is we should be vector B or, um, let's just say B one b two b three. Now, if we first look at the left inside and we applied the applied a matrix multiplication here, then we will have x one times the one the sex two times Be too us x. Three times v three. So this is actually our given. Give Alina the questions. Okay. So to figure out whether we have solution in this case. So the thing we need to notice that b one b two b three are all are all from our to space. So here we actually have this gives us I'll ride down to equations, two questions and three unknowns. So it's very clear that if we have to Lena equations with three unknowns. We have, even in many solutions here if we have three questions in three unknowns, and we can probably just solve their system as long as the system is consistent. But in this case, we have three unknowns and two equations than the system is always consistent and the the solutions will will not be unique. So that's the That's the

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