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In Exercises $3-6,$ the vector $\mathbf{x}$ is in a subspace $H$ with a basis $\mathcal{B}=\left\{\mathbf{b}_{1}, \mathbf{b}_{2}\right\} .$ Find the $\mathcal{B}$ -coordinate vector of $\mathbf{x} .$$$\mathbf{b}_{1}=\left[\begin{array}{r}{-3} \\ {1} \\ {-4}\end{array}\right], \mathbf{b}_{2}=\left[\begin{array}{r}{7} \\ {5} \\ {-6}\end{array}\right], \mathbf{x}=\left[\begin{array}{r}{11} \\ {0} \\ {7}\end{array}\right]$$

$\left[\begin{array}{c}{-\frac{5}{2}} \\ {\frac{1}{2}}\end{array}\right]$

Algebra

Chapter 2

Matrix Algebra

Section 9

Dimension and Rank

Introduction to Matrices

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University of Michigan - Ann Arbor

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

02:27

In Exercises $3-6,$ the ve…

01:42

In Exercises $1-4,$ find t…

00:41

01:24

$[\mathbf{M}]$ Let $H=\ope…

02:39

01:55

01:00

02:29

In Exercises $5-8,$ find t…

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In Exercises 1 and $2,$ fi…

03:02

So this question we want to find the be cordoned off this vector X in this, using the spaces so only to find he's buying parts in season one. And to that satisfies the situation by six, 2 11 Now, once again, you could do You could solve this on these through would choose something subversion and finds itself wants us to. Or you could just simply perform more operations on this matrix. Seven seats. Now, this is a pretty meet metric because he sues a two by three countries. Now, you should remember that we only have two confidence here. So all you really need is we're just really two by two. So you take this one and this one or this one or this one or this one. We just really need two of these three. Doesn't matter which one take. So I'm just going to take on st. So then one Fine, you know. Okay, Now I want to get from royal preparations to make this identity matrix, so let's take it. Well, one, I've been the AG three times over too. Thank you to go home. So then he gets 93 blustery, which is there? seven plus three times farmers 15 except possibly give you 22 Now 11 plus three times that you just live in. It has to be. The 2nd 1 remains unchanged. Now we will wounds 1 22 over one. And according to one zone ones, let's turn to which was it, huh? Secretary? Making change. Then you need tripped you Only one. What we're going to minus five because of one that gives you 01 Well, answer it is. It's about to. And so minus y times one. Do I respond? Plus five, huh? And then zero minus five times a heart, which is just 25 to now. Be careful. This is one here. So this is your season. One term and it's just He's so cute. Didn't see someone. Is he into Mama's five over too? Say so too. Is it too?

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