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In Exercises 1–4, assume that the matrix A is row equivalent to B. Without calculations, list rank A and dim Nul A. Then find bases for Col A, Row A, and Nul A.$$\begin{array}{l}{A=\left[\begin{array}{rrrr}{1} & {-4} & {9} & {-7} \\ {-1} & {2} & {-4} & {1} \\ {5} & {-6} & {10} & {7}\end{array}\right]} \\ {B=\left[\begin{array}{rrrr}{1} & {0} & {-1} & {5} \\ {0} & {-2} & {5} & {-6} \\ {0} & {0} & {0} & {0}\end{array}\right]}\end{array}$$

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

Calculus 3

Chapter 4

Vector Spaces

Section 6

Rank

Vectors

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then we have in the role equivalent metrics off. Here it is introduced. This is a truly clone form. Yes. Yeah, In Venice, Woman Bye. Is your all minus do five minutes 6000 So here we have in our stoke beautiful their rank. Well, that hair the ranking had to say, is the group. They're diamonds and all for no mark. Fix your hair, which is a total number. All by what columns in a Sen Roy equivalent metrics. We can see that the number of five elements our this from this. So there are two hybrid elements with the responding lee there, too. Uh, they were columns. Any. So therefore rank off is to hear now way have seminars to find out the diamonds. And so that is ankle long. Uh huh. No, not just here. So that's sort of the core. Do Uh huh. Mm n minus. Frankel. Hey. So here and is the number all, uh, Harlem's so here number of columns is for think of these two. This is equal to again. So the angle northern metrics Yes, to we have in us. Holds little Find out the basis. Oh, all right. Uh, huh? Room columnar Row another, which is a garland A. I can also from the markets here. That wow number of non zero. Uh huh. Rose in the store. The 1st and 2nd room on bond. The power, uh, elements are nivel stern. Second role. So the corresponding columns and here one minus one five horse toe, minus six. So this from the basis off our democracy? Yeah. Yeah. On the basis of rule, all our exterior will be the non zeros off the regular merchants. So these are one Sheetal. Then it's one wife hand zero minus two five minus six. Wow. So this way derived from the Roy equal and metrics, Which is this? No, we have toe find out basis off model that it's here to do that. Well, right. The reduce Rui clone Former, which is C. C will be after performing our prisons, we will have 10 minus 15 Single one. Minister of Ivory to three 0000 Yeah, you know this particularly with you know, there c 00 Looked like x one. Did you go three minus takes? Oh, and exposed will be by upon two x g plus Thanks. Very minus. Uh huh. Whoa. Mm hmm. Way have Venice, I explore. First she x four Next three. Next four. Uh, she really ever So here. Long the cases. No get. So here we look like one I bring to one Seattle. Honest by famous 301 the span off this toe vectors will give us this solution methods off. C x mhm.

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