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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}$$$\left[\begin{array}{l}{1} \\ {0} \\ {0} \\ {1}\end{array}\right],\left[\begin{array}{r}{-2} \\ {1} \\ {-1} \\ {1}\end{array}\right],\left[\begin{array}{r}{6} \\ {-1} \\ {2} \\ {-1}\end{array}\right],\left[\begin{array}{r}{5} \\ {-3} \\ {3} \\ {-4}\end{array}\right],\left[\begin{array}{r}{0} \\ {3} \\ {-1} \\ {1}\end{array}\right]$$

$\left\{\left[\begin{array}{c}{1} \\ {0} \\ {0} \\ {1}\end{array}\right],\left[\begin{array}{c}{-2} \\ {1} \\ {-1} \\ {1}\end{array}\right],\left[\begin{array}{c}{6} \\ {-1} \\ {2} \\ {-1}\end{array}\right]\right\}$

Calculus 3

Chapter 4

Vector Spaces

Section 3

Linearly Independent Sets; Bases

Vectors

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and this problem, we're given a sending electors knew where to find the basis for this that so let's form our system for big from the given lectures. Endless side of this matrix site is our system a CZ you can see hey has four rows and by colors. So it means that a mite hair enough given elements for Pete Rose, since the number of problems is greater than the number of rows. So we know that this system will spend the space. Um, next thing to do is to find the reduced role for or by this system and that Is he going to 1000 0100 000 Sorry. 0010 Negative one negative. 300 Negative to link two by two and zero. Since we know that this settled vectors, I'll spend the space Don't be basis. Dundee column Give its columns will be the basis for the system. Hey, what are you giving calls? The 1st 1 the 2nd 1 and the 3rd 1 will be our give. It holds so many faces where we set a will be the first told him off a 1001 The second column Obey negative to one negative one. And her column? Um A, which is six negative one, too.

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