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Determine which sets in Exercises $1-8$ are bases for $\mathbb{R}^{3}$ . Of the sets that are not bases, determine which ones are linearly independent and which ones span $\mathbb{R}^{3}$ . Justify your answers.$$\left[\begin{array}{r}{1} \\ {2} \\ {-3}\end{array}\right],\left[\begin{array}{r}{-4} \\ {-5} \\ {6}\end{array}\right]$$

the set of vectors in $(1)$ does not form a basis for $R^{3}$ .

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 that whistle of a form. Our system constant. Becker's that is one to make it three and negative. Four and five and six. So ready. So I went for this system can be written as well. 00 and 010 So, as you can see, we have the rolls, but two holes. So that means that, um, weekend ever give it element means roll right is the number of homes across. It means that this set cannot form a basis, and it can not spend this space. But it is a bit element in each column. So it means that this given set, this records are the nearly independent.

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