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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\}$$$\mathbf{b}_{1}=\left[\begin{array}{r}{1} \\ {-2}\end{array}\right], \mathbf{b}_{2}=\left[\begin{array}{r}{5} \\ {-6}\end{array}\right], \mathbf{x}=\left[\begin{array}{l}{4} \\ {0}\end{array}\right]$$

$[x]_{B}=(-6,2)$

Calculus 3

Chapter 4

Vector Spaces

Section 4

Coordinate Systems

Vectors

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Harvey Mudd College

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Idaho State University

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in this problem, we're given the basis to factors B one and B two and the Vector X and whereas to find recording it better, uh, we know that Rex Rex believe to see one. So the first elemental, coordinated vector most like first factor plus C two second element of quarters record most liked by the second phase is Victor. So from the first row, we know that forests see one plus five C two and from the second row, we know that's your musical See one minus six C two. So from the second row, we can see that C one is they could do *** three c two and a few years This. And if you like this in the first question we find that negative tree See two plus five C to visit before so to see two isn't comfortable for S C to Z two. And using this we find C one to be negative sense. So then I recorded it back to you will be negative six and two

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