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Let $\mathbf{v}_{1}=\left[\begin{array}{r}{0} \\ {0} \\ {-2}\end{array}\right], \mathbf{v}_{2}=\left[\begin{array}{r}{0} \\ {-3} \\ {8}\end{array}\right], \mathbf{v}_{3}=\left[\begin{array}{r}{4} \\ {-1} \\ {-5}\end{array}\right]$ $\operatorname{Does}\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ span $\mathbb{R}^{3} ?$ Why or why not?

since all three rows have pivot positions, then $\left\{v_{1}, v_{2}, v_{3}\right\}$ does span $\mathbb{R}^{3}$Check theorem 4

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 4

The Matrix Equation Ax D b

Introduction to Matrices

Oregon State University

Baylor University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

01:11

02:21

Let $\mathbf{v}_{1}=\left[…

02:31

Reasoning Does $\left(3 \f…

01:56

$\mathbf{A}=\left[ \begin{…

01:06

Let $$\mathbf{A}=\left[\be…

01:41

Is $\frac{1}{3}$ a zero of…

00:51

00:56

Write a convincing argumen…

03:18

03:35

08:59

All right. So for problems. Money too. We need to identify whether they given three vectors are whether they're given three vectors. Spend our three. So the key thing here is just too. This is just to identify whether these three vectors already nearing end it. If they're if they are in leaner independent, then we're that because leader independent three vectors will spend our three automatic. So right here. Um, we have we just the first form of this matrix A that is fanned by these three column vectors. So the first column, Mrs 00 Negative too. And zero negative. Three and eight. You and four negative one too far. Okay, um, now we interchange the first row and the third row so that this matrix will be in the Indonesian form. It will be elected to eight. Next five and zero. Negative. Three negative one and 004 All right. Now, if we consider the wiener system a X equals zero, then from the last rule, we have x three times four is zero. So rx three will be zero. And furthermore, from the second rule, we have a negative x two minus one x three that is also zero. But we already have. X three wishes zero So x two has to be zero and similar T r x one by the first row. I won't write down the exact question. You just need to know that x one. It's also zero. Then are our solution where the system will be zero Dr. So what does that mean? So that means it's Sheldon variable in the vector. Acts will not be dependent on each other because we get because we all if we consider the accent zero we the only solution is the trivial solution. So that means that those those three very goes will not will not be dependent on it around them. So that means spinoff. So that means he, uh, three vectors here we want to be three was been our feet. So where

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