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Repeat Exercise 25 with $\mathbf{v}_{1}=\left[\begin{array}{r}{1} \\ {2} \\ {-4}\end{array}\right], \mathbf{v}_{2}=\left[\begin{array}{r}{8} \\ {2} \\ {-5}\end{array}\right]$ $\mathbf{v}_{3}=\left[\begin{array}{r}{3} \\ {10} \\ {-2}\end{array}\right], \mathbf{a}=\left[\begin{array}{l}{0} \\ {0} \\ {8}\end{array}\right],$ and $\mathbf{b}=\left[\begin{array}{r}{.9} \\ {2.0} \\ {-3.7}\end{array}\right]$

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Calculus 3

Chapter 8

The Geometry of Vector Spaces

Section 2

Affine Independence

Vectors

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In mathematics, a vector (…

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03:40

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For Exercises $25-32,$ wri…

00:24

Perform each operation and…

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Use a calculator to perfor…

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01:01

01:04

03:12

In Exercises $125-134,$ so…

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00:51

we'll start by considering a general form of identifying combination. Off the victories Fee one for two on DFI tree. We're going to set this to be equal to a plus TV, which is a form of the points on the Given Ray. Now we can rewrite this expression. See, two times 15 minus V one plus e 3 10 ft, three minus. V one, minus teeth. Hymns. Fee on this is gonna be equal to a minus 41. So with the victory is given of et minus, we won 1/7 0 minus one. Feed three minus 31 is to a to, uh, minus fee. ISS minus 0.9, minus two and 3.7 on a minus. 51 is minus one minus two and 12. So now we want to find citizen three and t that satisfied this equation on? We can do that by reducing the following augmented matrix minus one. We understood. Well, Andi, once we reduce, we find the following sooner. 0.53 From here, we can read that. See? One is gonna be one minus 0.1 minus 0.5. That is 3.4 on this is because he to issue 0.1 C three issue 30.5 on T tops. T is equal to three. Do it. So now, with these values, we can go back to the first expression we had on board. We conclude that the point of intersection has is to ways off representing it, which is your 0.4 times 31 plus your 310.132 plus your 0.53 on also a plus three v this'll is the victor 2.76 on minus 3.1. Now we can see that all of the coefficients in this ah fine combination are positive. So, yeah, all these coefficients are known as a very centric coordinates, so all of them are positive on. This means that the point of intersection is inside off the triangle given by the victories Fee one video, be three

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