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Compute the determinant using cofactor expansion down the first columnDetermine the value 0f the first term in the cofactor expansion_ Substitute the value for a11 ...

Question

Compute the determinant using cofactor expansion down the first columnDetermine the value 0f the first term in the cofactor expansion_ Substitute the value for a11 and complete the matrix for C11 below:a11C1188Determine the value of the second term in the cofactor expansion. Substitute the value for a21 ano complete the matrix for C21 below:321C21Determine the value of the third term in the cofactor expansion: Substitute the value for 231 and complete the matrix for C31 below.331C31Complete the

Compute the determinant using cofactor expansion down the first column Determine the value 0f the first term in the cofactor expansion_ Substitute the value for a11 and complete the matrix for C11 below: a11C11 88 Determine the value of the second term in the cofactor expansion. Substitute the value for a21 ano complete the matrix for C21 below: 321C21 Determine the value of the third term in the cofactor expansion: Substitute the value for 231 and complete the matrix for C31 below. 331C31 Complete the cofactor expansion to compute the determinant. det A =



Answers

Use the cofactor expansion theorem to evaluate the given determinant along the specified row or column. $\left|\begin{array}{rrr}2 & 1 & -4 \\ 7 & 1 & 3 \\ 1 & 5 & -2\end{array}\right|,$ row 2

This is a question Number nine. We need to find the determinant off the metrics using charcoal. Right? So rightly call and forced. But here are three. You're minus minus two. And here, world. Right now. Any minute. Talk ornament for us pros to here on foreign. Do you want, right? No. Any minute told Solomon Second roads of years like that. You want to three? He wants thus no eliminate told Parliament her girl. So you're and I bet you want to. And here one full right will be easy for 23 here. One minus 12. Negative margin of any getting responsible. The duke of your glass tube. You never did. You weren't buying a six must for, you know, getting four minus two one minus 12. That is negatively, lover. You're negative or negative. Six thirties mega do seven. And your negative for navigating through that eats negative six. My never multiply by an 83. That is negative. 23 seven. Motive by two ladies 14 and six. Money by formed. That is 24. So be determined. All the metrics. He's negative. 71 right. Thank you

This is our question number 11. We need to find the determinant off the metrics using the first column. So for that, we need produced the sign ls minus and plus So you're de is a group last three eliminate for school and first rolls on your one dream three minus five. Your second tiny stsnegative. So you are a negative one. One for three, minus five. And your throat. Sinus positive reports that you do. 14 and 12 Now you're negative. Five minus six. Your negative five minus two early and here to minus four. Negative. Five minus six thirties When I get do it alone. Wordless fire that is 17 then doings for a student having a family member negatively level that is negative. Started to be last of a long line minus four. So the determinant is 82. All right, Thank you.

This is not a question of berate your determine, Andy, that is three. Multiply by one minus one, multiplied by here. Minus do right. So the determinant days three nurse to which is equal to why, right? Thank you.

All right, So now we have a new matrix A. And we need to calculate the determinant using the definition. Um, So I said in my explanation for question three that I was doing that one very technically. But this one, I'm going to do it a little faster. So what I'm gonna do is I'm going to right this again. And this is shown in your textbook as well. But I'm gonna write negative one for zero Teoh to to. So I'm just writing again. This part isn't writing it over here. All right, now I can put lines through here. Those are going to be positive, and then I'll have lines going the other way. Those are going to be negative. So determinative. A is negative. One times, two times negative. Three. So that's just that first red line goes through. Negative. 123 Second, red line goes through 4 to 2. Plus four. Teoh to plus. Now I go to the third red line one zero to minus. Now we go to the green lines 1 to 2 minus. So all the green lines are gonna be minus. Um, that's because the parody is negative for all of the multiplication that's indicated in the green. So that's going to be negative. One to to. And the 3rd 1 is four times zero times negative. Three minus. Okay, So we noticed that this one's with zero in it. They cancel out. And so now, negative. One times, Two times negative. Three. What's gonna give a positive six? Four times to his eight times two is 16 minus two times two is four plus negative Negus positive plus four. That's pretty convenient. So, um 16. 22 negative four plus four cancel out. And I guess I should show that I was doing that My brain Those go away. Okay, so let's try be I feel like we're gonna need a whole page for be, so maybe I'll come back to this page and do see, but let's go ahead and do be so Part B. We need to do the determinant using elementary row operations. Okay, so the first thing that I'm going to dio is I'm gonna multiply that first row by you know what? I really need to do that I'm just going to multiply the first row by two and add it to the third row. So that according to um postulate three, which says, If you add a multiple of any roto another row, then it doesn't change the determinant. So by postulate three now gives us the same thing. Negative one for one zero to to I'm taking the first role model, playing it by two and attitude it to the third row is going to give me zero. Eight plus two is 10 and two plus negative three to plus negative three is negative one. All right. Now, Also according to postulate three, I'm going to take the second row times negative five and added to the third row two times negative five. His negative 10 plus negative one is negative. 11. So our answer is negative. One times negative. 11 times. Two negative, one times to times negative 11 which is 22. Good. I got 22 twice now, so let's do see. All right, So, see, I'm going to do the determinant of this again. Negative one for one zero to to to to negative three. All right, So what I'm gonna do this time is gonna take this. And so the determinant of a is negative one times the minor, which is too, too to negative three. Okay, But this 2nd 1 I don't have a good way to a race. So I'm just gonna change my color for this one. I'm gonna have to put a minus in front of it, because the, um, co factor is going to have a negative term at the beginning. Negative one to the I plus J Power. This is gonna be a negative four times zero to to negative three plus whips. What? I just click lus. And now we'll do this one. This one is 0 to 22 one times 0 to 22 Okay, Equals, let me just write this in red Negative one times. Two times negative three. I'm just gonna dio this mine. Is this two times negative. Three is negative. Six minus four is negative. 10 so again, Two times negative. Three negative. Six minus four is negative. 10. Okay. Minus four times this. So I'm just gonna do this times this minus this Times this. Well, zero time negative. 30 minus two times two is four. So that's going to be negative. Four gay. Plus one times. This times, this mine is this times this? Well, zero times two is zero minus two times two is force. That's negative for okay, Negative. One times negative. 10 is 10. Um, negative. Four times negative. Four is plus 16 and ah, minus four. Which gives us 22. So again, I'm showing you faster ways for A and C that apply to a three by three matrix. Um, although really, what I did today and see also applies to a two by two matrix. It's going to get more complicated if you do a four by four matrix or greater. Um, but when we were doing part B, which is right here, I don't think there's, ah way to make that faster. You just you just do it. Thank you for watching.


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