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[M] In Exercises $37-40$ , determine if the columns of the matrix span $\mathbb{R}^{4} .$$$\left[\begin{array}{rrrr}{5} & {-7} & {-4} & {9} \\ {6} & {-8} & {-7} & {5} \\ {4} & {-4} & {-9} & {-9} \\ {-9} & {11} & {16} & {7}\end{array}\right]$$

Not in $R^{4}$

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 4

The Matrix Equation Ax D b

Introduction to Matrices

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[M] In Exercises $37-40$ ,…

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all right. So in problem 38 were given this matrix. Let's say a the first row is five. Next, seven, Victor four and NYU and second roll. We will be six and activate next. 75 There were over before Nick for an extra night connective night, and the last rule will be next to 9 11 16 5 So this is a four by four matrix on. We need to determine if the columns have matrix span are for so the first thing the first thing we need to do is actually count the number off people columns in this matrix. If actually the people columns are linearly dependent. If the the number of people columns equals equals four, then that means the column so off the basic span are for so well. First, I just I'll just write down the road, reduced to form off this matrix because it's, uh, it's kind of hard to calculating by hand. If you are familiar with the company's reputation, you can just use your prime Alva or programming skills to find that reduce station form. If you're not from here, I would recommend to just do this by hand and check your compare on your solution with me. And that will help you to, uh, get through the gate familiar with caution. Caution. Elimination. Okay, so the reduced lesion form will be one one one and 7/3 and negative 5/3 and for third. Other terms are zeros. So if we count the people positions here is one. Here's to three. So we have three people columns, which is less than the dimension off our three. And that's a same time you you want you can at the information that three people calls me his rank off, eh? Rank of a is three, but which is smaller, Definitely smaller than they even dimension off for. Sorry. Should be dimension off are for so the rank of A is three smaller than the dimension of our war, which is four. So that means columns off a do not spend are four

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