the-expansion-of-a-3-times-3-determinant-can-be-remembered-by-the-following-device-write-a-second-co

Question

The expansion of a $3 	imes 3$ determinant can be remembered by the following device. Write a second copy of the first two columns to the right of the matrix, and compute the determinant by multiplying entries on six diagonals:
Graph cannot copy
Add the downward diagonal products and subtract the upward products. Use this method to compute the determinants in Exercises $15-18 .$ Warning: This trick does not generalize in any reasonable way to $4 	imes 4$ or larger matrices.
$$
\left|\begin{array}{rrr}{1} & {0} & {4} \ {2} & {3} & {2} \ {0} & {5} & {-2}\end{array}ight|
$$

James Chok · Accepted Answer

in this example. We want to find the determines all the three by three matrix using this strip right here. So the first step to perform industry is we have to copy the 1st 2 columns. Yeah, to copy them over. We have zero for three, 35 and four. Then we&#x27;ll multiply down on these, diagnose and multiply up on these. So is there times five times? One gives you zero plus three times during times free, which gives you the right plus one times four times for which gives you 16 and who, minus by three times five times of one, which is 50 minus by four times. There are times right, which is doing minus by one times four times street, which should give you 12. This is 16 minus 15 miles to which is one months, 12 and six equal to my system.

James Chok · Answer

okay. In this example, we want to find the determines off this matrix using this trick right here. So the first thing we have to copy the 1st 2 rows First columns onto the right side. So have 123 33 and three. The multiplying the diagonals. And these diagonals we get one times three times to, which is six plus three times one time, three get in line. Plus four times. Two times three, which is eight times three, which is six times 4 24 minus three times, three times, for which is nine times for which should give you 36. Why does three times? One times one, which is three minus two times two times three, which is 12. So this is equal to 39 minus by 36 months. Three is 39 minus 12. So this is my soul.

Mark Augustyn · Answer

to find the determinant of this matrix. What we&#x27;re gonna use is common rotation. So we&#x27;ll repeat the 1st 2 columns, so we&#x27;ll have negative 20136 negative. 1.5. Then we&#x27;re going to multiply diagonals. If we go from the top down, we&#x27;re going to add these, and then we&#x27;re going to subtract the products as we go up. So the blue diagonals, we&#x27;re gonna take negative two times, six times negative two and then add three times two times one and then add four times zero times 1.5. They were going to subtract the pink diagonals. So minus one time six times for minus negative. 1.5 times, two times negative, too. And then, lastly, we&#x27;re going to subtract negative to time, zero times three. Okay, so anything with the zero is going to be zero. So that eliminates this one and the one at the end. And then as we multiply through negative two times, six times negative to would be positive 24 3 times to its six ah minus one time, six times four would be negative. 24 then no minus the negative. 1.5 times two times negative two would turn it at into six as well. So this would be minus six. So that 24 cancels with the negative 24 6 cancels with the negative six. So I&#x27;m left with the determinant of zero. Since my two since my determinant is zero, this would be a singular matrix.

Harry Evans · Answer

this question. We want to run the determinant office three by three matrix just to working with the first column. So we will start with the minor for the one of free and into two. So by doing this, we have eliminating the brain. Bacanovic Minor. We have the determinant off one minus for 36 on Mindless because we work in is Joice on the matrix, US minus, plus minus, plus minus on plus minus. Plus, there&#x27;s minus free and then the limit. Never in the current containing the phrase search minus free to three and six on, then with the two that&#x27;s a plus two. So plus two, limiting their own carbon containing the to touch minus three to on Andi brightness for and then I cochlear. The determinant of image makes metrics. We have one time. Six Just six plus 12 minus free and then minus. That&#x27;s minus 18 minus six. Andi hunters dropped this subsidence. No way! Um, enough. Hey, that&#x27;s 12 minus two. And then just simply work in itself is just 18 minus. And then that&#x27;s minus 24. Ah, for us too. 10. What&#x27;s your secret? 18 Minus 72 US 20. Fitch is equal to minus very for

Sriram Soundarrajan · Answer

everyone today we&#x27;re going to start problem about five heavy needs to find the determent off the three by three matrix which has given us to three minus tree four zero three, 615 So if you expand, why do they get They will be like minus three in the 20 minus 18 second element is zero into some value minus morning. Six press developed. So it comes to be like minus three in your tooth my last one in the 18. So it will be like my last 24.

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The expansion of a $3 \times 3$ determinant can b…

Problem 15 Easy Difficulty

Answer

24

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

Linear Algebra and Its Applications

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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

Kayleah T.

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

Linear Algebra and Its Applications