in-exercises-19-24-explore-the-effect-of-an-elementary-row-operation-on-the-determinant-of-a-matri-4

Question

In Exercises $19-24,$ explore the effect of an elementary row operation on the determinant of a matrix. In each case, state the row operation and describe how it affects the determinant.
$$
\left[\begin{array}{ll}{3} & {2} \ {5} & {4}\end{array}ight],\left[\begin{array}{cc}{3} & {2} \ {5+3 k} & {4+2 k}\end{array}ight]
$$

James Chok · Accepted Answer

So we want to find that Expect effect off, right. Operations on determinants on matrices. So first off to know, to see how we go from the first Matrix, the second matrix it&#x27;s simply row one k times everyone plus wrote you and we make that road too. So now taking their determined off the first matrix we get three times by four minus five times by two, which is told minus 10. So that gives you two. Now for the second matrix. For the second matrix, we get three times. Wife four plus two K minus, two times five plus three k. Okay, so this is eagle to 12 plus six K minus 10 plus six K. Now this six k and this six cancels out leaving, you told, minus 10. Which gives you two. We just same as our original answer.

James Chok · Answer

Okay, so we want to find the effect off. Right? Operations on determines. So to see how we go from the first Matrix to the second Matrix, it&#x27;s simply okay. Row one. And we&#x27;ve put that into one. So it&#x27;s just simply a re scaling off. Rose now taking their determines off the first matrix expanding across the first, right, it&#x27;s going to be one climbs by whole minus full monastery and one and there&#x27;s a zero. So we forget that and it&#x27;s going to be possible. Times by minus 342 and monastery. Okay, now leave that side doing the determinant for second matrix. We yet kay Time by four minus four minus 31 minus zero. And so we&#x27;re gonna forget that. And then plus Okay, it&#x27;s like minus three for two and negatives. Now, if he affected this doctor, the chaos or minus four minus 31 plus minus +34 Too negatively. Thank you. Now recognize that this term is the exact same thing as this one. Except there&#x27;s just a cane front of it. So always simply done is just multiplied the final determinants by K. When we perform this operation

Sriram Soundarrajan · Answer

101. Today we are going to solve problem number 21. Hear the term went off a the she the is Eddie minus B c you physicals determinant one the term rentals and right T c. Okay. The is a k T minus. KCB care d minus KBC, which is determinant. The disciples came into a T minus G c. Okay, in the tongue. And what later in the week owes.

James Chok · Answer

we want to explore the effects off the tournaments off Russian on the determinant. So first off, we should know how we got from the first Matrix to the second Matrix. Well, simply, it&#x27;s just taking road one. And we add que time by road to and we should do that to be right one. So then to Explorer, When we take the determines our first matrix, we seem to get a times what a D minus B times c. So now taking the determinant off the second matrix, we get a plus k c because my d minus b plus que de times my seat So this is a d plus k c d minus me. See, plus K c d. You notice that this and this time capsules So you&#x27;re left with a D minus B c and therefore he has no effect on the makers

Ebubekir Akta? · Answer

First of all, there are three basic properties off our operations and that effects determined off our metrics. 1st 1 is swapping two rules when we screw up at two roads off a metrics on the sign off Determinants the change Second twenties multiply by a constant Ah riel Constant Ah, on that multiplies determinant by okay And the 3rd 1 is ah substrate act a multiplier If I roll, that does not change the world you offer Matt determinants with these properties way will be able to solve this problem. The 1st 1 we see that the first time to the first and second trust are swapping s so we can say the determinant The sign of a determined change. Ah, the retirement off first mattress is a d minus B c On the second twenties CD minus baby. We can see that on the detainment eight equals two minus determinant A right. I was in the second floor. Ah, the operation is way at first wrote, Ah, the remote flight My key, the second throw and at onto the first row on So we can say that I have determined will not change in the next one on the road operations is Ah, we multiplied the seconds wrote on by a constant K on. So we can say that the determinant will be multiplied by K. That&#x27;s fixed it que times determined a will be determined April in the next one. Their operations is, um, multiple light the first road by K and ah to the second rule the term months. I will not change the next one. The operation is swapping first and second through and the term month Sign off a determined will change on the last one on the road operation is a multiplication off her first role by K, so the tournament will be multiplied by Kate. That&#x27;s all for this question.

Sriram Soundarrajan · Answer

everyone today we&#x27;re going to fall. Problem number 19. Yeah. A data meant off a B C pretty is heady minus B C a d minus busy. Let it be into town. And what determinant off. See the uh huh Leap is see the minus 80 C b minus. Hey, he just determinant Took so determined. One equals minus off determinant.

Problem

In Exercises $19-24,$ explore the effect of an el…

Problem 22 Easy Difficulty

Answer

row replacement no effect

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

Linear Algebra and Its Applications

Grace H.

Catherine R.

Heather Z.

Caleb E.

Absolute Value - Example 1

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row replacement no effect

Linear Algebra and Its Applications

Grace H.

Catherine R.

Heather Z.

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.

Catherine R.

Heather Z.

Caleb E.

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

Linear Algebra and Its Applications