in-exercises-33-36-verify-that-det-e-aoperatornamedet-eoperatornamedet-a-where-e-is-the-elementary-m

Question

In Exercises $33-36,$ verify that det $E A=(\operatorname{det} E)(\operatorname{det} A),$ where $E$ is the elementary matrix shown and $A=\left[\begin{array}{cc}{a} & {b} \ {c} & {d}\end{array}ight]$
$$
\left[\begin{array}{ll}{1} & {k} \ {0} & {1}\end{array}ight]
$$

Sriram Soundarrajan · Accepted Answer

different today. We&#x27;re going to solve problem number 33 here to do Tom and is given by one. Okay. Zero lot determinant off is given the uh huh. The see the so he will be equals a plus. Casey B plus Katie seat The determinant off e equals a press case into the minus B plus Katie into city 80 plus k c V minus BC Linus K. D. C. So it it&#x27;s like a d minus b c. Then this is a This is it determinant off equals what return mint off equals a T minus busy So determinant off e equals determinant off into the dominant off.

Sriram Soundarrajan · Answer

great. We&#x27;re going to solve a problem. Number the foot here. The government is a because mhm b c think it takes equals the 011 Seattle So determinant mhm equals zero minus one. The physicals minus one. So then e equals 0110 into a B C B, which will be getting it does seat the mhm the so determinant off. Yeah, equals C B minus 80. What we should be C minus 80 determinant off. Hey, because a T minus b c so determinant off and in the pit dominant off mhm equals minus learn Hindu A T minus B C to be B C minus 80.

James Chok · Answer

Okay, so in this question, we want to figure out who want to show that determinants off E a is equal to determinant off e time flight attendants off, eh? So, working on the left hand side. First, we have to first figure out what ee A&#x27;s. This is 10 k on a B C. D. So one times they give you a plus zero times. See, which uses a one times B plus zero times e excuse would be zero times a plus. Kate M. C. Which is this Casey zero times b plus Que Tom ze, which is just Katie todo determinants. Oh, hey is equal to Okay, well, eight times, Katie, So K a B minus. Casey turns me so K B c. So Okay, plans were a D minus, Casey. Okay, now the term it&#x27;s off, eh? Is equal to eight m c minus anytime soon and determined off E is just one times K one times. Can&#x27;t give Luke a minus zero times here. Is it just k and determinants old, eh? 10 by 10 minutes, we&#x27;ll be is just came from a the artist B C, which is the exact same as determined

James Chok · Answer

Okay, so we want to verify That&#x27;s determinant off E a secretive determinant off e Taiba. Determinants off, eh? So first figuring out what e times is we have one times a plus zero times. See? Excuse you, eh? One times B plus zero times the which gives you be and K Time&#x27;s a plus one time see, which gives you a k A plus c and then you have keytones B plus one times D, which gives you K B plus d. So then the determinants off e A. It&#x27;s simply a became be rusty. One isn&#x27;t b a k a pussy, which is K A B plus 80 Marchioness k a b plus B c this term cattles at this time. So you&#x27;re left with a D minus. BC now taking the tenements. All these disability, we get it&#x27;s evidence. Oh, he&#x27;s even to a D morning specie. The Turners off e is equal to one times one giving you one k time or minus by Kate. I&#x27;m zero excuse zero. This is one. So then determinant. Oh, aye. Was by 10 minutes off e years, even to a d on a species, which is the exact same as taking the tone int off, Peter

James Chok · Answer

So in this question we were verified That determines off a B is equal to determine it off eight times by the tenement off beat. So let&#x27;s work the left inside out first. So a be is it 23 minus 16 months to okay for three months. One month street, Just you. So this is three times four is 12 miles. Six. That&#x27;s six. Three times three is nine minus six and three is 18 which is collected nine negative one time by four minus two times one. So that&#x27;s negative for months. Makes awful plus two. So that&#x27;s negative too. And negative. One by three, which is negative. Three plus six. Excuse you three to determines. Oh, baby, is it into six and three, which is 18 minus negative to pass by 99 which is just 80. So what is this your now the tenements? Oh, aye. Is it 23 times by minus two, which is negative. Six minus six times modest one which is 96. So what? You are and the tenements wouldn&#x27;t really need to Catholic This spot all his tablet four times on minus three which is negative, tall and three times, right? Minus one, which is negative. Three. And this is negative. 12. Sastri is 90 line. And so tone INTs. Oh, aye. Times by determines. Don&#x27;t be using which is there anything as atonement?

Nez Nikoo · Answer

Okay, Um, this problem is asking to find the determinant of a inverse off a basically. So this really is the easiest have seen out of all the problems so far this formula, you need to know this formula that the inverse of a determinant a is one over determinant. A. So all we have to do simply is no to determine A In this case, we know because that&#x27;s what they&#x27;re saying is three. So he&#x27;s 1/3. That&#x27;s really the answer. There&#x27;s not not mawr to it. For some reason, they give us determine that B is equal to minus four. But they&#x27;re not way. We don&#x27;t need to do anything with that. That&#x27;s it. So if you know the formula, you know, determined of a all you have to do is just plug the numbers 1/3. That&#x27;s it. Thanks. Bye.

Problem

In Exercises $33-36,$ verify that det $E A=(\oper…

Problem 33 Hard Difficulty

In Exercises $33-36,$ verify that det $E A=(\operatorname{det} E)(\operatorname{det} A),$ where $E$ is the elementary matrix shown and $A=\left[\begin{array}{cc}{a} & {b} \\ {c} & {d}\end{array}\right]$
$$
\left[\begin{array}{ll}{1} & {k} \\ {0} & {1}\end{array}\right]
$$

Answer

the property $\operatorname { det } ( E A ) = ( \operatorname { det } E ) ( \operatorname { det } A )$

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

Linear Algebra and Its Applications

Grace H.

Heather Z.

Kayleah T.

Maria G.

Absolute Value - Example 1

Absolute Value - Example 2

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the property $\operatorname { det } ( E A ) = ( \operatorname { det } E ) ( \operatorname { det } A )$

Linear Algebra and Its Applications

Grace H.

Heather Z.

Kayleah T.

Maria G.

Absolute Value - Example 1

Absolute Value - Example 2

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

Grace H.

Heather Z.

Kayleah T.

Maria G.

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

Linear Algebra and Its Applications