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For the matrices in Exercises $17-20,(a)$ find $k$ such that Nul $A$ is a subspace of $\mathbb{R}^{k},$ and $(b)$ find $k$ such that $\operatorname{Col} A$ is a subspace of $\mathbb{R}^{k} .$ $$A=\left[\begin{array}{lllll}{1} & {-3} & {9} & {0} & {-5}\end{array}\right]$$

a. $k = 5$b. $k = 1$

Calculus 3

Chapter 4

Vector Spaces

Section 2

Null Spaces, Column Spaces, and Linear Transformations

Vectors

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University of Michigan - Ann Arbor

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in this problem, we're s to find value case like that. No, it is a subspace in our to decay in the column. A subspace in our cake so hard today. No es. So as you can see, our has one roll. And 12345 colds. Right So than a ISS one by five. Um, makings. So since this no way. We're looking, uh, percent of recreational perform eggs, is it zero and now is on my eye and no. Yeah, we're looking for eggs here. That X should be open for five. Fine. One or five by one reason is the number of columns and a should be cooking number Rose in are, uh, eggs majors. So from this case should be five then l A is the subspace pain or fine part. Be cold, eh? So this time work creation looks. There's also perform exit B. So a CZ again one, my fine. Now we know not be a cz fine by one from front, eh? So since the number of Poland's and a mixes with the number rose in eggs, we want I have a problem and the resulting medics will be up to size one by one. So from this Okay, Is these what I call a maze of subspace and or

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