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In Exercises $15-18,$ find a basis for the space spanned by the given vectors, $\mathbf{v}_{1}, \ldots, \mathbf{v}_{5}$$$[\mathbf{M}]\left[\begin{array}{r}{-8} \\ {7} \\ {6} \\ {5} \\ {-7}\end{array}\right],\left[\begin{array}{r}{8} \\ {-7} \\ {-9} \\ {-5} \\ {-5} \\ {7}\end{array}\right],\left[\begin{array}{r}{-8} \\ {7} \\ {4} \\ {5} \\ {-7}\end{array}\right],\left[\begin{array}{r}{1} \\ {4} \\ {9} \\ {6} \\ {-7}\end{array}\right],\left[\begin{array}{r}{-9} \\ {4} \\ {9} \\ {-1} \\ {0}\end{array}\right]$$

$\left\{\left[\begin{array}{c}{-8} \\ {7} \\ {6} \\ {5} \\ {-7}\end{array}\right],\left[\begin{array}{c}{8} \\ {-7} \\ {-9} \\ {-5} \\ {7}\end{array}\right],\left[\begin{array}{c}{1} \\ {4} \\ {9} \\ {6} \\ {-7}\end{array}\right]\right\}$

Calculus 3

Chapter 4

Vector Spaces

Section 3

Linearly Independent Sets; Bases

Vectors

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in this problem. We're given a set of bikers and no work but as to find the basis or that Viper. So let's first for our system that is formed by our vectors and blessed side. This system, as I mentioned size for by pictures, be more B two B three before and fire. So first thing, too. Look at this. We have five rolls, one to triple five. So mentioned saying his five rows and five holes. So since number of rose is equal number of problems, you know that this electors will spend the space. Why is this information important? Well, because since we know that the specter will spend in space, we consider that the given problems off the system will be the basis Becker's. Okay, so we're actually looking for the basis factors off a So let's look at the reduced role equipment for off the system. So then you're ready. Tropical form. Our system will look like 10 00001 000 I heard 2000 00100 and or 3rd 1/3 Negative. Once you're here, so we help you ever tell him you won't have a element here. We have our second favorite element here in the particular element here, so our first you would tell them, would be the first color. Second will be the second column, and our first poll will be the fourth column in the orginal system. A. So then, the basis for this set of electors will be the first column all metrics. A negative 876567 in the second column. Age negative seven Negative mind negative 57 and then the or column, which is 1496 names except

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