compute-the-determinants-in-exercises-9-14-by-cofactor-expansions-at-each-step-choose-a-row-or-col-5

Question

Compute the determinants in Exercises $9-14$ by cofactor expansions. At each step, choose a row or column that involves the least amount of computation.
$$
\left|\begin{array}{rrrrr}{4} & {0} & {-7} & {3} & {-5} \ {0} & {0} & {2} & {0} & {0} \ {7} & {3} & {-6} & {4} & {-8} \ {5} & {0} & {5} & {2} & {-3} \ {0} & {0} & {9} & {-1} & {2}\end{array}ight|
$$

Sriram Soundarrajan · Accepted Answer

Even today we are going to fall. Problem number 13 He given Matrixes five by five toe Cool Really minus seven three. Minus fight. Still several toe. Cyril several servant three minus six. Cool minus eight five zero five Toe minus three. Feel theory nine minus one. Oh, so we have to expand along second row, so it will be like minus two Hindu determinant off four. Perform attics for zero three minus fight seven 34 minus set five zero toe minus street zero. Set up minus one. But then we can expand along the for true 00 minus one. So what will be getting will be like minus two. Hindu minus off minus warm into the term. Lent off for Cyril minus fight What? Plus seven three minus eight 50 minus three. Then plus minus two. Indu determined off. 40 three, 734 five zero to then 0050 Again, if we expand what will be get minus two Window one and do we can expand along Second column. So plus minus. Plus it will be three in do minus 21 Verse 25 minus two window saying we can do a long three three. Indo eight minus yeah. Off a minus two Windows three in do 13 minus two. Indu seven 39 minus 42. It will be six.

James Chok · Answer

Okay, so the question is to find the determinant off this matrix biker fact expansion. Now, if you don&#x27;t know by now, we will always come back to expand by the row or column with the most gear is in there. So in this case will do this road. We could do this. Pollen. Does it really matter? No chance, Dan. Why I asked you to go back to the previous questions, and I explain why. But the basic idea is that these zeros cancels out the determinants. So it&#x27;ll be easier for us to do. Now. We have to remember all signs. So this position being for one so being negative now we could also remember it by a positive. And then when you move one a possible one down, it&#x27;s switched sides. So positive. Negative, positive. Negative. So we get negative, too. Times by the determinants. Off. 3 to 400 minus for 10 minus 5671 23 to 0 Compactor expanding by this column. Positive. Negative. Positive. Negative. Positive. Negative. So we negative one have a negative, too. Turned by the determinants off. 3 to 40 minus 4123 and two. So what we get is too negative. Two time negative one gives it to times by. So Okay, in fact, expanding by this road you could do about this, Colin doesn&#x27;t matter. I&#x27;ll just do. By this way, you got a positive negative, too negative. So it&#x27;s positive. Negative. Four times by the determinant off 342 and two minus one times by the determinants off 3 to 2 and three. So this is going to be two turns by four times. Two times three, which gives us six minus two times for giving you ate. But major full minus by one times three times three, which gives you nine minus two times two, which gives it for So this is two times by native for six months. Eight is native to as a native to minus Phi. One times nine times for my minus four, which gives you five. This is two times by eight minus five, which is two times three. Excuse me. Six

Sriram Soundarrajan · Answer

going today We&#x27;re going to solve for the number nine. So here is given us for by for metrics for 00 five 17 toe minus five than 300 zero than 4 to 1. It&#x27;s like eight three one seven. So we have to expand along the withdraw Third row element is like 3000 So do you, like, plus minus plus minus only minutes Expand off three, three Indo. Then metrics actually list these two fast two rows and then this will come. So deal black 005 seven toe minus five 317 So this value will be like three in do It will be like plus minus plus so five in the seven minus six like 15

James Chok · Answer

Okay, So the question asks us to find a determinant of this matrix. Why? Co fact that expansion so on this otherwise told you will always perfect expand by the row or column with the most zeroes. In this case, you will always be this road. So you see why First off, let&#x27;s remember out signs. This is in a opposition being to one. So this will be negative. This is an even position. So it will be positive. This is negative. This is fun in a cold fact that expansion along that road is going to be negative. Zero time. Buy some meat, some determinants, plus by zero times with some other determinant minus three times with some determinant plus zero times Lesson terminus. Now, it&#x27;s not really important. What these determines our because we have zero try by some number to this number will always be there. This is always benefits. This is forced down to zero again. So you&#x27;re only left with, uh, this matrix. Now, if you look at what that matrix is, it&#x27;s going to be one minus 22 to minus four by to zero and five. So you get this matrix by removing this column and this work. So now we&#x27;re left to find a determined off this matrix. So we have to cope, act excited again and carefully Take Stan was cool Now, remembering our science, it&#x27;s also this is the opposition so negative and positive And this is maybe too so he&#x27;s gonna negative three times by minus two times by the determinant all to y two and five plus by minus four, tied by the determinant off 12 two and five minus zero Time left some matrix. So negative three has, like negative too. I have two times five, which gives you 10 minus two times five, which was a 10. So that becomes zero minus four times one times fight, which gives you five minus two times two, which gives you for And then this is also zero and said this not and so we have minus three times by zero minus four times by one plus zero, which is just 93 times in a beautiful I just simply so

James Chok · Answer

to the question us us to find a determinant off this matrix using code factor expansion. Now, unless otherwise told, you should always go fact expand by the row or column with the most zeroes. So in this case, we&#x27;re probably going to expand either by this road will of this court because they have the same about zeros. And in this example, I&#x27;ll just expand through this road. You can expand by this color. You should get the same result. It doesn&#x27;t really matter, but I&#x27;m just gonna expand by the road. So you have three times by minus 200 630 84 minus tree times y o sudden net minus zero times by the 10 minutes off some matrix plus zero times by the determinants off some matri&#x27;s miners there are turned by the determined off some matrix. So the reason why we expand by the row or column with most zeroes is because you essentially will get a lot of zeros because this is zero Tabassum number. This is zero Tabassum number is zero Tabassum number. So all of the last three terms become zero. Yes, he comes here and you&#x27;re left with just one big determinants left to do so just sold this determinant. We once again used perfect expansion. Now, because there&#x27;s you can&#x27;t once again could expand by this road Or you can expand by this college. Does it really matter? I&#x27;m just gonna expand by this world once again. So you have three terms by negative two times by the determines off 30 for ministry plus zero times but determined off some matrix. But the virus this year, you mind, And this is plus zero times with some matrix and he&#x27;s become zero again. So this is three times, like minus two times by three times and 82 3 which is negative online minus four times zero is zero, which is just going to be three times, like minus two times five minus nine, which is need to six times by negative nine, which is 54

Sriram Soundarrajan · Answer

Hello, everyone. Today we are going to solve problem number 11 here they given for both. I&#x27;m in Texas three five sick minus six for zero minus two three minus street zero zero one foot and 000 three. So we had to expand along the food through. So it will be like less minus, plus minus minus, plus minus. Plus so three and do three five minus six zero minus two three 001 So it will be like three Indu learn into minus six. So we will get like three into minus six, which is a call to minus 18.

Problem

Compute the determinants in Exercises $9-14$ by c…

Problem 13 Medium Difficulty

Answer

6

Related Courses

Linear Algebra and Its Applications

Related Topics

Discussion

Top Algebra Educators

Grace H.

Anna Marie V.

Alayna H.

Caleb E.

Algebra Courses

Absolute Value - Example 1

Absolute Value - Example 2

Recommended Videos

Watch More Solved Questions in Chapter 3

Video Transcript

David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications

Grace H.

Anna Marie V.

Alayna H.

Caleb E.

Absolute Value - Example 1

Absolute Value - Example 2

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

6

Linear Algebra and Its Applications

Grace H.

Anna Marie V.

Alayna H.

Caleb E.

Absolute Value - Example 1

Absolute Value - Example 2

David C. Lay, Steven R. Lay, Judi J. McDonaldLinear Algebra and Its Applications

Grace H.

Anna Marie V.

Alayna H.

Caleb E.

David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications