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[M] Repeat Exercise 43 with the matrices $A$ and $B$ from Exercise 42 . Then give an explanation for what you discover, assuming that $B$ was constructed as specified.

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Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 7

Linear Independence

Introduction to Matrices

Campbell University

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

00:17

In Exercises $37-44,$ perf…

01:34

00:55

01:43

02:31

01:37

00:45

00:13

01:47

Find the following matrice…

01:53

GEOMETRY For Exercises $37…

Um so in this in this video, we're going to solve that work. I'm going over harder to problem number 44 from section 1.7, which is on a linear independence. I'm not actually going to do the calculation here, but I'll just go over how to do the problem. So basically, this might work from question number 42. Sorry. This might work from question number 42 which I did to find B and B is just made off the linearly independent columns or the pivot columns of a A CZ. The other columns give a free variable, which makes the entire set to be linearly dependent. So be is made up of four pivot Collins. And, uh, what the problem is essentially asking us to do is solving the argumentative eight Matrix B V. Where V is either column three. We're calling five of Victory, our matrix A that we that was not used in the construction of B. So if we if we solve this matrix by setting it up, um, either But with be bar, uh, the third column or the Fifth column, then we would we would see that the, um the echelon form of this matrix would have four pivot columns again for because he is just made of of the pivot columns of A, which means that every single variable in the assistant system equations let's label each column with a B c D. This means that a nominal matrix is just a um it's just essentially a system of equations that were solving, um, based for variables, the number of variables based on the number of column. Becker's There are so here four column vectors represents four variables. So, um, at the end, we're gonna have four pivot columns with all the positions, right? That's why they're called poop columns. Which means that the resulting right side of the equation we'll be the solution. Thio B X equals V, which means that X is unique since every column as a pivot. Colin and B uh, which means that V is spend. Are these in the span of the columns of you? Okay, so he is in a span B one b two, B three on. Before that is what we find out and

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