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

the given set of vectors spans $R^{3}$

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 truth and this system using that word. What? There's looks like this. So this system and ready to roll echo for your 010 001 And, Nick, you're too negative. One hell do you want? Uh, so we have three rows and or colmes. And as you can see, how long given element here won't give it element here. Element here. So we have a deal element for each role. So it's me. In fact, this sad actually forms a basis, and it spends the the space. And as you can see, we have three defense furs, second and third column in the rock Registrar. Excellent form. So it means that 1st 2 factors birth three or the nearly

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