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In Exercises $5-8,$ find the coordinate vector $[\mathbf{x}]_{\mathcal{B}}$ of $\mathbf{x}$ relative to the given basis $\mathcal{B}=\left\{\mathbf{b}_{1}, \ldots, \mathbf{b}_{n}\right\}$$$\mathbf{b}_{1}=\left[\begin{array}{r}{1} \\ {-1} \\ {-3}\end{array}\right], \mathbf{b}_{2}=\left[\begin{array}{r}{-3} \\ {4} \\ {9}\end{array}\right], \mathbf{b}_{3}=\left[\begin{array}{r}{2} \\ {-2} \\ {4}\end{array}\right], \mathbf{x}=\left[\begin{array}{r}{8} \\ {-9} \\ {6}\end{array}\right]$$

$x_{B}=\left[\begin{array}{l}{-1} \\ {-1} \\ {3}\end{array}\right]$

Calculus 3

Chapter 4

Vector Spaces

Section 4

Coordinate Systems

Vectors

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Okay, We have given be one equal stove one minus one today and B two equals two minus 349 And the trick was to Tu minus 24 And the solution X is 89 six and we have to find Coordinate, Rector. Okay, so we will solve it by be even We do B three Sequels, Toe X. Okay. So we can revive the execution like one minus terry toe and minus one for minus toe minus 394 And this will be aired minus nine six. Okay, so we have to solve this for solving days. We'll go first in r two equals tow R one plus R two. So what we get is one minus tree, too air. This will be zero. This will be one. This will be zero on This will be minus one. Okay. And this will be saying minus 3946 And now we will do what we will do. R three equals toe three r, one plus artery. Then we get one minus story too. And 010 minus one 00 10. 30. Okay. For which we can easily say that. Then she three equals to 30. It means si three equals 23 and C two equals two minus. And for solving this for their we can say see, even minus three. C two plus two equals to eight. And so even plus three plus six equals toe eight. So see, even will be eight minus nine. That is minus one So we can get. Finally, next week we'll store X base B was to C one, C two and C three and that will be minus one minus 13 And that is over. Final answer. Thank you.

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