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In Exercises $1-4,$ write $\mathbf{y}$ as an affine combination of the other points listed, if possible.$$\mathbf{v}_{1}=\left[\begin{array}{l}{1} \\ {2} \\ {0}\end{array}\right], \mathbf{v}_{2}=\left[\begin{array}{r}{2} \\ {-6} \\ {7}\end{array}\right], \mathbf{v}_{3}=\left[\begin{array}{l}{4} \\ {3} \\ {1}\end{array}\right], \mathbf{y}=\left[\begin{array}{r}{-3} \\ {4} \\ {-4}\end{array}\right]$$

$y=\frac{13}{5} v_{1}-\frac{2}{5} v_{2}-\frac{6}{5} v_{3}$

Calculus 3

Chapter 8

The Geometry of Vector Spaces

Section 1

Affine Combinations

Vectors

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for this question were given the wan to be deep also Won soo zero vite suit to be recalled to true minus 67 under Envied three to be equal to 43 warn why equaled so minus 34 minus four. I want to write Why, as a fine combination of the other points. So to start waits we computes the translated points The transit of points v two minors v Want, which is won't minus feeds on seven. You do a victory minus v Want, which is 31 Juan. And they do why miners ve worn, which is minus for LSU minus four. Next we find skill Oz seats Sue century Such nuts. Seats to veto Miners v. Juan plus seat Ori Victory Miners v. Juan. You want to know why miners v one We do this by we reduce This implies are reduced The augmented metrics with this points as the cool. Um so the matrix will be one minus eads seven three won't warn minors for sue minus full. You want to put this street land here? Just tow, give the points but it doesn't matter when you roar would use these. So when you reduce these, you're gonna have 10 minus two over five zero Juan minus six over 5000 So we see that difference. Consistence under this is like seats sue on dhe seat during Sami's. See two equals toe minus two over five on. Then sit. Three quarto Minor. Six over five. So this implies that seed so equal to minus two over five on. Then see the records of minor six over five when you plug us into the question of why miners view want equal toe citrus minus two over five off Vizio Miners v Juan minus that city theory victory Miners we want when you solved a CZ you off white quartz fits in over five. We want minus tsu over five V two minor, six over five. The three.

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