mathbfm-is-it-true-that-operatornamedetaboperatornamedet-aoperatornamedet-b-experiment-with-four-pai

Name: mathbfm is it true that operatornamedetaboperatornamedet aoperatornamedet b experiment with four pai
Uploaded: 2019-08-02
Duration: 1 min 6 s
Channel: Numerade
Description: $[\mathbf{M}]$ Is it true that $\operatorname{det}(A+B)=\operatorname{det} A+\operatorname{det} B$ ? Experiment with four pairs of random matrices as in Exercise $44,$ and make a conjecture.

Question

$[\mathbf{M}]$ Is it true that $\operatorname{det}(A+B)=\operatorname{det} A+\operatorname{det} B$ ? Experiment with four pairs of random matrices as in Exercise $44,$ and make a conjecture.

James Chok · Accepted Answer

So the question asks is determined off 80 equal determinants off a multiplied by the determinants off being. And so to find out, we will generate 35 5,000,000 Measure C&#x27;s on most planet together and see what happens. So I pray a pilot script right here, and you could just run this on an online i. D. So what&#x27;s basically does is he sets a to be around or five or five matrix and is said to be to the amount of 55 entries can&#x27;t place the difference between the determines off a multiplied by the term that&#x27;s all be. And then we&#x27;ll subtract by, determines off a multiplied quietly return. It will be so. Then it will print. True if the difference is less than some lumber. Otherwise we&#x27;ll print force. So basically what this size is if the if the difference between them is really the s&#x27;more, basically almost zero, then you will print Cherie. Otherwise, you&#x27;ll prove false, and the result when you perform this program is sure

Nicholas Barvinok · Answer

We want to verify that for two by two matrices A and B that the determined of a times B it was the determinant of a times the determinant to be alone. Let&#x27;s just fix to arbitrary two by two matrices So a B C D multiplied by, well, normal&#x27;s a B C D. Call that a and be will be F G h k perhaps J. We don&#x27;t want eyes, but Jay&#x27;s okay, actually, I was okay too. Let&#x27;s do I f g h I skip tea. So the determined of well, let&#x27;s let&#x27;s first find the product So a being by matrix multiplication Where we get we get a F plus b h a g plus b i cde f plus de age C g plus d I. And from this we get that the determinant of a B is a f plus. The h times C g plus the I&#x27;m minus a G plus the eye times cf waas the age And on the other hand, we get that the determinant of a times The determinant of B is a D minus. BC, multiplied by f i minus gh and this gets us If we expand everything a loose a D death I minus a d g h minus B c f i plus B c g h. Now let&#x27;s actually expand the determinant of the product on another pain because we are running out of room so we get determinant of a times B is a F plus B H time CG plus D I minus a G plus B I times cf plus the h And if we expand this, we get a F C G plus a D I plus B h c g plus b e h d I minus a g c f minus a g d age minus b i c f minus b i d h. So let&#x27;s see, Does anything cancel? Yes, we have a f c g a f c g here. So these to cancel we have be hd I hear and be hd I hear. And now we have four terms. FBI plus B H C G minus a g D h minus. B I c f. So here we have positive a deify here we have a positive i d. If I Here we have a positive B c g h. Here we have a positive bcg age. Here we have a negative 80 th nated h gh. And here we also negative B i c f negative b i c A. So this formula does hold for two by two matrices and we&#x27;re done.

James Chok · Answer

okay. In this question, they want us to Catholic. Various determinants using determined off A&#x27;s 93. The tenants will be is negative one and a b r a b awful. Therefore, major cities, it&#x27;s official tournaments off, baby, we can sell records out 10 minutes off, eh? 10 minutes. I&#x27;ll be so, which is negative? Three has a negative one, which is one be determinant. 085 So this is simply to be determined O b plus 5 to 5, which is native one the fire, which is disconnected one. So to understand that, wise to the fire or you simply do is he simply continually take out the fire every time Basically, performance step five times Would this be And you get the 10 minutes off beat fifth native 1 to 5, determined off to a oh, to A is equal to 22 to the engine. In this case is for determinants off, eh? Which is children? Four is potent force their 16. It&#x27;s a negative. Three. Six am Street is 24. So negative 54 determinant all a transpose b A. So this is determined off a transfers tells my determines will be I have a determinant away now determined off a transpose is just simply determinant off a. So it&#x27;s native three. That&#x27;s why negative one negative three, which is negative. Night it terminals. Oh, be in verse a B. If you haven&#x27;t done this earlier in the earlier questions, you can figure out that did term you. This is eager to determines all. Hey, this is just simply determined. Okay, which is negative story. You don&#x27;t know the reason why it doesn&#x27;t exercise earlier on in the other questions and you can see why this is

Sriram Soundarrajan · Answer

here. He needs to prove to determine Gaby. Is he called retirement? A interview that might be classifying. It is a good it b c d and be physical. It&#x27;ll e f de hit. So the down And indeed it time that the first we&#x27;ll find that. Hey, do take Dominick be It comes to be a T minus B c. I didn&#x27;t do being too, my dear. This is Louise. A B e it minus a, uh, minus B c it plus B c f d. Okay, no, you will find Dichter A B. It is a car e plus bt then if plus b it c e plus DT then cf plus d hit So determinant off a big what? We&#x27;re big hunting, but you in Colorado e plus bt can do cf plus d it minus c e plus d d in do if plus B it incidentally comes to be a CF plus he be it b d c f b d be it see if see it yet minus the deep. If the d b it. So if we subtract word out into a sea of these two things go then BDD, it&#x27;s bdb it the beauty is distinct. Credible then Okay, he&#x27;s for the remaining is like a d it plus BG CIA My enough c b It&#x27;s minus the Z for ah dd if the d e f business. OK, then, CB it&#x27;s TV. It&#x27;s okay. Idiot. Idiot. Easier made it. Okay, so these brought it.

Robert Daugherty · Answer

created to problem 45 that give us three matrices A b and s and they tell us that s inverse A s is equal to be and they ask us, must A and B be equal And the next question is must the determinative a equal that determine it be so let&#x27;s start with a determinate question. If this is the condition I&#x27;m given, then I know that the determinate of s inverse a s has to equal the determinative Be That means the determinant s in verse times the determinant of a times The determinant of s equals a determinant of B. Let&#x27;s just say that the the determinant of s in verse is called. That s one. So the determinant of I&#x27;m sorry we back up was called a determinate of s we&#x27;ll call that s one. So the determinant The inverse is just one over s one e determine it a times s one. This is just the terminate of a and it must equal the determinate it be So this is a true statement The determinant of a must equal the determinative Be Now let&#x27;s just take a look at what we have in the other situation s inverse a s is equal to be so let&#x27;s motor by both sides by s and then that gives me a s z Quito s b. And then if I multiply by s as in verse equal SPS inverse. This just tells me that a the secret to SB as in verse. So it is not true. That is you got to be so it is not necessary that a is equal to be in this condition. So given the condition we started with, I do have the determinants must be equal but the matrices air not necessarily equal to each other.

Problem

[M] Construct a random $4 \times 4$ matrix $A$ wi…

Problem 45 Easy Difficulty

$[\mathbf{M}]$ Is it true that $\operatorname{det}(A+B)=\operatorname{det} A+\operatorname{det} B$ ? Experiment with four pairs of random matrices as in Exercise $44,$ and make a conjecture.

Answer

Not true.

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

Linear Algebra and Its Applications

Grace H.

Catherine R.

Caleb E.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

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Not true.

Linear Algebra and Its Applications

Grace H.

Catherine R.

Caleb E.

Kristen K.

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.

Caleb E.

Kristen K.

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

Linear Algebra and Its Applications