compute-the-determinants-in-exercises-1-8-using-a-cofactor-expansion-across-the-first-row-in-exerc-3

Question

Compute the determinants in Exercises $1-8$ using a cofactor expansion across the first row. In Exercises $1-4,$ also compute the determinant by a cofactor expansion down the second column.
$$
\left|\begin{array}{rrr}{2} & {-2} & {3} \ {3} & {1} & {2} \ {1} & {3} & {-1}\end{array}ight|
$$

Sriram Soundarrajan · Accepted Answer

everyone today they are going to start problem number third here. We had to find the determinant off the Given three by three matrix that is two minus two three, 31 to and one three minus smart. So expand along. Second column to like minus off minus two. Indu minus three. Minus two plus one into minus two minus three. Minus three in new for minus nine. So it comes to be to win. Do minus five plus morning. Do minus five minus three into minus five. Value is zero.

James Chok · Answer

So you will find the determinants off this matrix using Cho Phat expansion across the first row. So remembering how signs it&#x27;s going to be positive, negative and positive. So the answer is going to be Well, how we do it is by four times by the determinant off 03 minus two by minus by one times, by the determinant off 433 and five plus two times by the determinant off 403 and minus two. So this is four times zero tumble, quite double zero minus negative. Two times. Wife free, which is negative. Six minus one times, four times five. Which gives you 20 minus three times street. Which gives you mine plus two times by four minors Time. I&#x27;m negative too. Which gives a connective, eh, Minus three times they&#x27;re giving you zero. This is four times by six minus one times by 11 plus two times. Like negative eight. This is 24 or 24 minus 11 minus 16 which should give you negative three

James Chok · Answer

So in this question we will find the determinants by a co fatter expansion only across the first, right? So once again remembering our science, it&#x27;s positive, negative and positive. So very simply, it&#x27;s going to be. Why Times by the determinant off. Three minus tree minus four and seven, minus five minus two. Find bythe 10 minutes off. Zero minus tree Chu seven. Plus Fly to plant by the determinant off +032 and minus four. So long to be five times three times seven, which gives you 21 minus by well for native. Four times on negative. Three Gives you positive. 12. That plus 12. My soul native native time linked. It gives you positive. So plus two times zero times seven, which gives you zero minus two times by my ministry, which gives you minus six now, plus two times zero times minus for, which gives you zero minus two times three, which gives us six. So this is going to be five times by nine plus two times by two negative mix of politics, so it&#x27;s going to be two times six six and minus two time by six, which is simply 45

Sriram Soundarrajan · Answer

Today we are going to solve a problem. Number one here. We need to find the determinant off. The Given three by three Matrix matrix is 304 toe, three do and 05 minus one there to expand the law. Second column. That&#x27;s what has the in question. So it will be like minus zero and do some value will be against zero does three Indu minus three plus zero, then minus five. Window six minus eight So it&#x27;s result will be minus nine plus 10 which is equal to one.

James Chok · Answer

Okay, so we want Thio find a determinant off this matrix using expansion across the first road and then we&#x27;ll find it by the second caller. So the first thing that we have to do is to record to remember what the signs up. So if you want to expand over the first road, it can&#x27;t be positive, negative and positive. So we have zero times by the determinants off when we removed the road and color off 3031 and then it&#x27;s negative. Wonderful. Minus full tons of determinants off 502 and one. And finally, it&#x27;s a plus sign under one time, by the determinant off five minus 32 and three. So this is zero multiplied by voxant determinants that this is zero. So you can stop that in this advice for time by the determinant, which is by time by one minus two times zero plus one times five times three minus two times like native three. This is four miles four time bye bye plus five pounds Freeze 15 15 plus six which is equal to 20 What? Minus 20 plus 21 which is simply one Now if you want todo an expansion on the second column. We have to remember that this is negative. This is positive. And this is negative. So the easiest way to remember is this is 11 The position of this block 11 and one plus one is two even. So, some positive. This is one to which is through one plus two years. Three, This is going to be negative. And this is 22 which is four. So it will be a positive. This is 32 which is five. And so we need to. So you will have minus four. Tether the determinants off 50 to 1 plus by minus three kinds. Like the determinant off your one Jew one in minus three times is your one five and zero. This is minus four times by five times one plus two times zero minus three times zero times one minus. Two times one minus three time. Zero times there, minus five times one. And this is minus four times by five. Minus three times minus two and minus three times minus five, which is minus 20 plus six plus 15 which is equal to one

James Chok · Answer

Okay, so we want to co factor expand the determinant by the first right on Dwight&#x27;s second column. So first thing that we should remember is our science. So this this is positive. This is negative. This is politics. So the determinant is simply one times by the determinants off 11 for two, minus two times by the determinants off 312 and two satisfy four times by the determinant off 312 and four. So one times one times two gives you two minus four times one, which is for minus two tired by three times to, which gives us six minus two times one, which gives you two just four times, three times for kitty 12 minus two times one which is to So this is one times by minus two minus two times life for plus for time about 10 which should give you 30. Now if you want to expand, why the second column? We should remember our signs again. So this is negative, positive and negative. And so we have Negative, too. Times by 312 and two Suss buy one times by one for two and two, minus by four times 143 and one. Now, this is minus two times three times to which gives you 61 is two times one giving you too, just one time. One time to give it to minus two times for which is eight minus four time that once has one, Which gives you one when those three times for which gives you 12 So which is minus two time by four plus one times by minus six minus four times like minus 11 which also gives you 30.

Problem

Compute the determinants in Exercises $1-8$ using…

Problem 3 Easy Difficulty

Compute the determinants in Exercises $1-8$ using a cofactor expansion across the first row. In Exercises $1-4,$ also compute the determinant by a cofactor expansion down the second column.
$$
\left|\begin{array}{rrr}{2} & {-2} & {3} \\ {3} & {1} & {2} \\ {1} & {3} & {-1}\end{array}\right|
$$

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

Linear Algebra and Its Applications

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Alayna H.

Caleb E.

Kristen K.

Absolute Value - Example 1

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Linear Algebra and Its Applications

Anna Marie V.

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Absolute Value - Example 1

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

Anna Marie V.

Alayna H.

Caleb E.

Kristen K.

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

Linear Algebra and Its Applications