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In Exercises 11 and $12,$ use an inverse matrix to find $[\mathbf{x}]_{\mathcal{B}}$ for the given $\mathbf{x}$ and $\mathcal{B} .$$$\mathcal{B}=\left\{\left[\begin{array}{l}{4} \\ {5}\end{array}\right],\left[\begin{array}{l}{6} \\ {7}\end{array}\right]\right\}, \mathbf{x}=\left[\begin{array}{l}{2} \\ {0}\end{array}\right]$$

$\left[\begin{array}{c}{-7} \\ {5}\end{array}\right]$

Calculus 3

Chapter 4

Vector Spaces

Section 4

Coordinate Systems

Vectors

Johns Hopkins University

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

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In mathematics, a vector (…

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In Exercises 11 and $12,$ …

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In the following exercises…

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In Exercises $13-18,$ use …

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In Exercises 30 and $31,$ …

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Given $A$ and $b$ in Exerc…

in this problem. We're given a basis in defectors that form the base is so we have B one and B two and were given an expected and we're has to find the coordinate director. So we know that X is equal to P. B, sir. Change important methods. But like by the court in Vector and from this, we can say that then the coordinate factor is equity universal PB times multiplied by a factor X What's PB PB still lamented metrics formed by defectors that for at basis beat So it is or fire and 67 So from this we find P being worse to be negative seven over to three five over to the naked too. And to find the coordinate factor, we're gonna both fly pt nurse with the given X vector and refined according it's better to be negative. Seven Fine

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