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Find the determinants in Exercises 5–10 by row reduction to echelon form.$$\left|\begin{array}{rrrrr}{1} & {3} & {-1} & {0} & {-2} \\ {0} & {2} & {-4} & {-2} & {-6} \\ {-2} & {-6} & {2} & {3} & {10} \\ {1} & {5} & {-6} & {2} & {-3} \\ {0} & {2} & {-4} & {5} & {9}\end{array}\right|$$

6

Algebra

Chapter 3

Determinants

Section 2

Properties of Determinants

Introduction to Matrices

Missouri State University

University of Michigan - Ann Arbor

Lectures

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Okay, so we'll find a determined by reduction. So the first couple road action steps that will do is we'll go right to and we're plus two times everyone. So that in to shoot up the rights. The Greek. Sorry. Three. And then we'll go full minds by one deck into four and finally go right. Five. Modest migrate to dancing five. That gives The Matrix won three months. One of your mom's too 02 months. Four months, two months. Six. So now who performed the first reductionist? I'm sorry. This is your negative. Six plus six. Get easier to minus two. Gives his three plus zero times to stage three, 10 miles, 4 to 6. Now the next step and you do one minus. Once again, this is your five ministry kitty to negative six. Modest. Minus one gives a connected by June. My zero could do to negative three minus two. Gives you modest. Well, yeah, I'm extra doctor. Step two, this is 00 negative for minus minus four gives you 05 minus minus two gives you five plus 27 And finally nine plus six gives you 15. No, we will do rope for my cyber too. And put that into a fool. And we'll also do by five minus seven on three times by rose three incidental. So let me get the Matrix. This is unchanged minus 10 minus two. You're two months. Four months, Two months. Six is your 36 Now, this is the first operations to to my studio zero negative five minus minus four. So that's months. 12 minus minus two. That gives you native one minus my six. So that gives you five, then, is it second operations? Now, this is your and we have 15 plus 15 minus seven on three times +67 on three times six is 14. So 15 minus 14. That gives you one. Now we will swap Row three. And so that was for. And that means we have to put a negative inside. Outside of what determinants? Most G? No, to my for my street. My six zero is your minus one or by 00036000 What? So this is an upper triangle, a matrix. So the determinant is the product of a diagonal. So negative one tends to double a minus one time. Bye. 321 which is negative. Negative six. So it's just six foot six

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