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Question

Let $A=\left[\begin{array}{ll}{3} & {1} \ {4} & {2}\end{array}ight] .$ Write 5$A .$ Is det $5 A=5 \operatorname{det} A ?$

Sriram Soundarrajan · Accepted Answer

Hello 20. We&#x27;re going to solve a problem. Number 37 here. My took a equals three one for so five A is equals to 15. Fine 20 right. Determined off five is equal to 1 50 minus 100 which physicals 15 five in the determinant. A calls. So I even do 86 minus four five in the two, which is so five Indian determined A is not equal to determent off. Find it.

Robert Daugherty · Answer

Section three to Problem number 30. They give us a matrix A. And they tell us that the determinant for Matrix A is equal one and were asked to find the determinant of matrix B. So the key is what is the transformation to get from A to B? What does that transformation do to the determinate? So if you start out with a B C D. So let&#x27;s describe the transformation. Well, it looks like the A&#x27;s and the B&#x27;s are on the bottom, so it looks like Row one was interchange with Road to And then what happens? It looks like we multiply Row one by three and it looks like we mortar pyro too by four to get to three c three D for a four b. So this is the transformation that takes me from a to B. So what is the effect of switching rose? Well, that puts a negative one on the determinant. Multiplying a row by three means the determinant is multiplied by three. Multiplying a road by four means the determinant is multiplied by four. So the determinant of B is going to be negative. One times three times four times the determinant of a So this is just negative. 12 is the determinant of beef

Robert Daugherty · Answer

section three days to problem number 32. They give us a generalized two by two matrix a sick with a B C D. They tell us the determinant of this matrix is one. And then they give us a matrix B that is formed from a transformation of and ask us to find the determinate. Be so the key to this is just sort of unlocking the puzzle. What is the transformation that takes you from A to B? So it looks like what happens is columns air switched. So it looks like column one is interchange with column, too. So that would give me be a D. C. It looks like, uh, we&#x27;ve multiplied row one, but negative one. So that gives us negative b negative A. And it looks like on the bottom room we took What? Um, so it&#x27;s negative four times, row one plus road to and created a new row, too. So that would give me, um, de minus four B and C minus for a So that is the transformation. So what things that we do in the transformation that effect terminate. When you switch the columns, you&#x27;re gonna multiply by negative one when you multiply that row by negative one. Also multiply the determinant by negative one. So the determinate of B is going to be negative one negative one times the determinant of a term of a is one. So this tells me the determined it be is also equal to one.

Robert Daugherty · Answer

section 3.2 problem 29. They give us a two by two matrix a two by two matrix B. They tell us the determinant of a is one and find the determinate be so the key years to find What is the transformation that happened to get me from A to B. So if I started out with Matrix A So a is a B C D. If you look at in matrix B, it looks like there&#x27;s a C here instead of a B. Um, and there&#x27;s a be here instead of a C, so that looks like there&#x27;s a transpose that happened. So if you were to transpose that matrix that would get you a C B D, then what is the transformation that would take you further? What would happen if I did negative two times Row one than that? Transformation would end up with what negative to a negative to see. And what if our to take the other transformation would be three times Row One plus wrote to that would give me three a plus B and then three c plus de. So that&#x27;s the transformation that gets me from A to B So we got to see what did these transformations. What effect did they have on the determinate? Okay, well, the transpose has no effect because the determinant of a is equal to the determinant of a transposed. Okay, so that did that made no change for me. Um, and then if you take, um, multiplied one row by negative two. Okay, So multiplying that row by negative two, that&#x27;s going to change the determinate by negative too. Um, if I did this where I multiplied a row and then added to road, that doesn&#x27;t change the determinant. So what I can do? The only thing that affects the determined here was multiplying that row by negative too. So if the determinant of a is equal toe one, then the terminate a B is going to be negative too. Times the determinant of a So this is gonna be negative to So again, I just think he is to look at the transformations. Transposing the maitresse had no effect on the determinant. Multiplying by two negative too did have effect on the determinant. Combining Rose did not have any effect on the determines that the only thing that affected this was that multiplying the road by negative too

Thomas Emment · Answer

okay. Given our major cities and be on the to be minus 38 equals matrix hair. What are possible values for little A. So we got some traction here between the teammates sees now we&#x27;ve got a plus or minus operation between matrices. Please do is take each corresponding element, do the operation. So in this case, it will be so. Could we want to find a really to worry about the first row first element here. So we&#x27;ve got seven minus for a plus B, and this will be equal to the to hit now. It was a constant unfriendlies, or scales you can call them. Scales are always do is times we each individual element by the scaler. And that&#x27;s fine. So that&#x27;s, um that&#x27;s right. Out. We only borrowed, really, But our first row first elements, You won&#x27;t find this A Okay, so the two big the first few moments we 14 to us that we have minus three lots of what&#x27;s here. So minus three times four between minus 12 a month, three times five minus 15. Okay. And this is old, equal to two. Okay, so 14 minus 15. Well, that&#x27;s gonna be minus one say about 12. A minus one equals two on ones besides got mice 12 a is equal to three. And so a should be equal to minus 3/12. What? You could divide talking about by three. You&#x27;ve got minus 1/4. Okay, make a match.

Wesley Hines · Answer

were asked to multiply the following skip maitresse e by the scaler of five. When you multiply matrices by a skill early, multiply every term inside the major seat by the scaler, so this would be the same as negative. 15 5 10 Negative 40 negative 10 and negative 25.

Problem

Let $A=\left[\begin{array}{ll}{a} & {b} \\ {c} & …

Problem 37 Hard Difficulty

Let $A=\left[\begin{array}{ll}{3} & {1} \\ {4} & {2}\end{array}\right] .$ Write 5$A .$ Is det $5 A=5 \operatorname{det} A ?$

Answer

5 det $A \neq \operatorname{det}(5 A)$

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

Linear Algebra and Its Applications

Anna Marie V.

Kayleah T.

Maria G.

Michael J.

Absolute Value - Example 1

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5 det $A \neq \operatorname{det}(5 A)$

Linear Algebra and Its Applications

Anna Marie V.

Kayleah T.

Maria G.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

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

Anna Marie V.

Kayleah T.

Maria G.

Michael J.

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

Linear Algebra and Its Applications