let-mathbfv_1leftbeginarrayr-3-0-6endarrayright-mathbfv_2leftbeginarrayr-2-2-3endarrayright-mathbfv_

Question

Let $\mathbf{v}_{1}=\left[\begin{array}{r}{-3} \ {0} \ {6}\end{array}ight], \mathbf{v}_{2}=\left[\begin{array}{r}{-2} \ {2} \ {3}\end{array}ight], \mathbf{v}_{3}=\left[\begin{array}{r}{0} \ {-6} \ {3}\end{array}ight],$ and $\mathbf{p}=$ $\left[\begin{array}{r}{1} \ {14} \ {-9}\end{array}ight] .$ Determine if $\mathbf{p}$ is in Col $A,$ where $A=\left[\mathbf{v}_{1} \mathbf{v}_{2} \mathbf{v}_{3}ight]$

Gideon Idumah · Accepted Answer

for this question with a church if p is in the column off, eh? To do that, we must ensure that a X your calls a p most off his solution. So how do we do this with a check? If the augmented metrics or commended metrics A He&#x27;s consistent. So a P will be minus three 06 minus two. Sue three zero minus six, three one 14 minus nine cause this is speedy. No. What we do is we try to reduce these. We introduce your S O U C for all three equal to rule three. Lost to warn. This will put a zero on than its days. So why we do that? We&#x27;re gonna off minus three, Sue, so remind us too. 01 zero Sue minus 6 14 Then when you do this, you&#x27;re gonna off zero minus one three, minus seven. So next we try to introduce zero on the native. This true, that is, make these zero. And then to do dot She just 03 You called Zorro? Three plus off through Sioux on. This is gonna give minus three minus two zero one zero minus two minus 6 14 And then When you do this, you&#x27;re gonna out 0000 so we can see that. Look at this. Look at this. So we can see that this is Constance is consistent. So we see Dr the documented metrics. The augmented metrics correspond. So a consistent system through a consistent system. So this implies that P is in colon off, eh?

Lucas Finney · Answer

All right, So for this problem, we&#x27;re giving our matrix. Negative. 11 negative. 20134 to 0. We wants to find a squared, a cubed, and we want to determine if it satisfies this given equation here. So setting up to find a squared We can only really do this by doing the matrix multiplication. So I&#x27;ve already have I already have that set up there. Now we go through. And as a reminder, we do matrix multiplication by taking the dot product each element i j in our matrix. So row I, Colin J. Is going to be the dot product of the I throw of a with the Jays column of a So element 11 is going to be a negative one times negative one. So we&#x27;ll have positive one in there, plus zero times one plus four times negative. Two would have one. Ah, minus eight. That&#x27;s going to be negative. Seven. Then elements to one going to one times negative one. So negative one there, plus one times one. So zero plus two times negative. Two will have negative four in here. Element 31 Don&#x27;t be negative. Two times negative two. That&#x27;s going to be positive, too, plus three. So five plus zero times needed to. We&#x27;ll just have five in there. Element 12 is going to be negative. One time zero, but zero times one plus four times three. So it&#x27;s just 12 element to two going to be one time zero plus one times one. So we have one plus two times three. So one plus six that&#x27;s going to be seven. Element 32 is going to be negative to time. Zero plus three times one plus zero times three. So it&#x27;s just gonna be three in there than Element 13 is going to be negative one times for. So it gives us a negative four zero times to you plus four times zero. So that&#x27;s just negative. Four element to three is going to one times before, plus one times two. So that gives us six plus two time zero. So that&#x27;s just going to be six in there. And then Element 33 is going to be negative two times for negative eight plus two times or sorry three times to. So that&#x27;s negative. Eight plus six gonna be negative, too. Next to find a cube. We have to multiply what we have there by a again. I&#x27;m just gonna copy and paste that down there, grab you and bring you down there. Okay? So continuing along doing our matrix multiplication would have negative one times negative. Seven going to give us a positive seven plus zero times negative for so still positive. Seven plus four times five who have positive. Seven plus 20. Yes. Plus 20 is going to give us a 27 in there than element to one is going to be negative. Seven minus four. That&#x27;s negative. 11 plus two times five. So plus 10 negative. 11 plus 10 is going to give us a negative one in there. Element 31 is going to be negative. Two times negative. Seven. Just 14 plus three times negative. Four. So we have 14 minus 12 plus zero times 5 14 minus 12 is going to give us two in there. Element 12 is going to be negative. One times 12. So we have *** 12 plus zero times seven. Still name 12 plus four times three. So have negative. 12 plus 12. So it&#x27;s gonna be zero in there l&#x27;m in 2 to 21 times 12 plus one time 7 12 plus seven is going to be 19 plus two times three. So we have 19 plus six is going to be 25 than element three to be naked two times 12. So that&#x27;s negative. 24 plus three times seven, which is 21 of negative. 24 plus 21 plus zero times three. So negative 24 plus 21 is going to be negative. Three, then element 13 negative. Two times negative. Four positive. Eight plus three times 6 18 So we have 18 plus eight. And then lastly, we have zero times negative to. So you have. Um Yeah. Positive. Positive. Eight plus 18. They&#x27;re going to be 26 element. Um, to three. He&#x27;s going to you one times. Negative. Four. Let&#x27;s six. Which is going to give us a to there, Then plus two times Negative, too. So we have two minus four is going to be negative too. And element 33 negative. Two times negative for positive. Eight plus three times six. What a moment. Here. Okay, Yes. So you&#x27;d have and negative two times. Negative. Four positive. Eight plus three times six. So we have positive. Eight plus 18 which is then going to give us 26. Uh, one more. My mistake. I thought that 26 looked familiar. I had made a mistake for calculating that 13 element. So 13 should actually be negative one times negative for so positive for plus zero times six positive. Four plus zero plus four times negative. So we have a positive four minus eight. That should just have been a negative for their and that gives us our A cubed. Now we need to check if it satisfies this equation up here. Well, we have a cubed, so I&#x27;m just gonna copy and paste him down. Then we have a paced him down, and then we are going to be subtracting off 26 times the identity matrix minus matrix with 26 on the diagonal, six on the diagonal and zero everywhere else. So this guy here is going to give us Well, we have 27 plus negative one minus 26. That&#x27;s 27 months. 27 is gonna be zero negative. One plus one plus 00 tu minus two plus 00 zero plus zero minus zero zero 25 plus 1 26 minus 26 0 negative three plus three minus zero is zero negative. Four plus four minus zero is zero negative. Two plus two minus 00 26 plus zero minus 26 is zero and there we have it.

Thomas Emment · Answer

okay. We weren&#x27;t in seven or eight times be its unique modification. We do the rose off the Matrix. Private colleges, the 2nd 1 So, for instance, if I went to find, you know what I said was fine. Second row here. First column we go. Second row, First column one times three is 33 times minus minus three. So it&#x27;s gonna be zero. Now, let&#x27;s take the second row. Second column one times minus takes. Queen minus two times. One times 333 months, two is one. Okay, Now we want the top, right? I&#x27;m going to stop in a second. Comment. Like mixing this up instead of, you know, 1112211212 tickets. So you go 12 here. So but 1 to 2 times zero on here. Got 123 months. 11 time stories three and then modesty to be a whoops. We&#x27;re actually identity here. Nice

Fan Yang · Answer

full caution. A. We&#x27;re looking for the products off a P. So it&#x27;s how well be so First of all, we write downs and magics One birth, because there&#x27;s a one shoe one would and then right down the magics be This is the are free when you chew and, uh, we calculate it is well be one times zero class, two times one and there one time three purse two times two The secondary role. I&#x27;ll be one tons, zero class, one ton street and there won times Oh, sorry. It&#x27;s a secular Oh, well, Giza when part one times Verapaz won tons work and they&#x27;re one town story plus one times two. So the s around B zero plus two and a straight class four three pass to the aura past one and it&#x27;s the final lesson will be to sever 45 for the problem. Be way looking for so a green, you see? So first of all, we got to the answer off a peon there for either question A. The answer is true. 715 And then we&#x27;d write down the magic. See, Is the world like your four? Well, one tender we calculated by the same way. It&#x27;s a true times weren&#x27;t past seven times one and UH, two times nicked in four plus seven time for for the second row is a worm password. One times weren&#x27;t wasthe. First time swarm and the one times 9 to 4 past five times one shows. Answer. Wealthy to past seven Thank you eight past seven and thus far looked in school class fired and as a final after while being my don&#x27;t have word sex and aware for the question, See, really look youthful, We&#x27;re looking for a plastic be How is she the products off a plus B in the sea? So first of all, we calculates the A plus B. It&#x27;s a world be what your guns are. Magic. So a first and the class is a magic speak and the answer will be 15 truths Rick. And then we can calculate birth Charles who? Well, the paradox awful. A Cosby and the Sea. It&#x27;s a will being re first writes down the ass off a poss B from sir to risk me and it happens magics and see if one elected for or one Phil. We do the same thing as we&#x27;re in class one when Time for class, five times a one and, uh, word times next four plus fun times. Well, and the two times were class three times World two times 9 to 4 Clause three times one fan, sir. Calculate it as no up you. One plus five victim full crossed. Five true pasts re elected eighth class three and the final as well be 615 may be terrified.

Harry Evans · Answer

when we went to find the invest off 39 Teoh six. The first thing we want to do is find the determinant off. It&#x27;s to buy geometric, so determining a is equal to two times three times six is 18 minus two times nine, which is also 18. As we consider determinant is there were, which ultimately means that the investors and exists. This is because when we find on new, um, in verse, we have to multiply by one over determinant on gorgeously if you multiplied by zero, that means the inverse is ever so it doesn&#x27;t exist.

Doruk Isik · Answer

in this problem. We&#x27;re giving the metrics. I don&#x27;t need words. Tiu term whether seventies and pulled a war isn&#x27;t know. So let&#x27;s look at the augmented system for by A and w So that is a negative six. Make every 12 6 to 1. So, um, reduced role echo for this system. Looks like one name to negative. Won&#x27;t carry 000 That is You can see here from your Oh, uh, already show Echo all of these metrics. This system, it&#x27;s consistent. So it means that dummy is o. K now to pass for No way we&#x27;re gonna multiply a devil. So negative six negative 3 12 6 Bye bye to one. We get native six times two is 12 bust wealthy zero negative. Three times to his negative. Six plus six. We have zero. So we got the zero vector. So it means that is no

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With $A$ and $\mathbf{p}$ as in Exercise $7,$ det…

Problem 8 Easy Difficulty

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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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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

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

Linear Algebra and Its Applications