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A| Jcon: 0 o1 d Homework: 0 Hw L (7.1 7.217 1 dace 1 L8...

Question

A| Jcon: 0 o1 d Homework: 0 Hw L (7.1 7.217 1 dace 1 L8

a| Jcon: 0 o1 d Homework: 0 Hw L (7.1 7.21 7 1 dace 1 L 8



Answers

$\left[\begin{array}{rrr}-1 & 0 & 7 \\ 3 & -5 & 2\end{array}\right]\left[\begin{array}{r}6 \\ -4 \\ 1\end{array}\right]$

But when we multiply a matrix by a three by three identity matrix, we know that for any matrix, any square matrix from out the size I multiplied by any magic. A. We know that the counter is just a so for our answer in this question, Wimal to play in the three by Three Matrix by an identity matrix. Therefore, our answer just stays the same as my three 12 zero one minus one, 257 And that is our answer. Women want to pry it by the identity matrix.

I only have a matrix A. As the Matrix 0 -27 five four, negative three. And be the matrons 840 zero 14 Now first thing we want to find here is a plus B. Finding a Polsby just means add the parts that go together. So I had the top left with the top left, the middle with the middle, the top right with the top right. And then so on zero plus eight gives us eight. They have two was forced to 707 On the bottom 505 four Plus 1 is five. Three plus four is one. So that's our major. It's A plus B. No a minus B is very similar. So if we subtract instead So in the top left, zero mindset is -8. They have to -4 is negative soups 7 -07. On the bottom 5 0 is five. 4 -1 is three. And I give 3 -4. There's negative stuff not for the matrix to A. That just means take every component in a multiplied by two. Mhm. And so this becomes zero. Now you're four 14 10, eight -6. That's our matrix to a. We have three. B is very similar to just take everything and be multiply it by -3. So it's 1924. May have 12 zero zero nee of three. No, you have 12.

So on this problem, we're given this matrix and were asked to use matrix capability of a graphing utility to find the determinant. So I went to Desmond's dot com and went to math tools matrix calculator and got this matrix calculator. So I have a four x four matrix. So I go new matrix And I got four rows and four columns And the first entry is a zero and then a minus three in an eight and that too. And then eight one a minus one and six And then I -4 in a six. Mhm and zero and a nine. And then uh minus seven, two, zeros zero, zero and 14. They had dinner now to find the determiner of this, I use the D E T button right here go determine it a matrix A And there it is 7000 441 7441.

In this video, we're gonna go through the answer to question number 21 from chapter 9.5 so as to find the fundamental Matrix or a fundamental matrix Thio the Matrix Different equation. A X prime equals a Times X where is and Tricks, which had three by three matrix given here on this upright. So it's fine fundamental matrix for this equation. We're gonna have to first find the three Aiken values and then find their respective I come back to us and then from that we conform the from Dimension Matrix. Okay, So to find the Eiken values we look at the matrix a minus r I find this. It's evident. So we have minus, uh out into the leading diagonal. And then you get this matrix. Okay, so expanding the determinant along go minus our times by right. Do you want to matrix and seven, uh, minus one times by two by two matrix a turban and 01 87 minus R. Okay, so this is gonna be minus, uh, close by s. So this is gonna be minus seven. Uh, plus, uh, squared. Close 40 minus zero times. Somebody. Sorry. Zero. Uh, then minus minus eight is plus. Okay. This is gonna be a cubic polynomial. It's gonna be minus R cubed plus seven. Uh, squared. Minus 14. Huh? Close aides. This could be fact arised into, uh, minus one minus two for minus R. Okay, So when that's equal to zero, they would just read off The Eiken values which are are is equal to see one, two, and four. Okay, It's not gonna find I'm vectors associating with those Ivan values. So we do that by looking for a vector you want, but satisfies a minus. One times I was one of the first I can tell you. Touched by a defector you want. I think it's there. I want this a Linus I look like Well, it looks like AA minus one 10 zero minus 11 eight minus 14 six times by you, Which we could write Capone wise as X. Why is that? He was there. And then this is us. The quite easy. Just read off. What's wise that need to be. There's look at the top row with the matrix. Ah, that's basically saying the minus one times x plus y zero. So if x is one that why must be equal to that that one as well. And then looking on the second row, if wise one then accept and said it also one. So, uh, factor is just one more want. And you can substitute those values of X y zed into the bomber off the metrics just to make sure that that works on. Of course it does. So move on to the second item. Specter, It's associated with Ivan. Value are equals two. So the same process a minus two I it's gonna be minus 210 zero minus 21 AIDS minus 14 five. Okay, most probably by BET you two, which will rise. Likewise. That. Okay, so again, we can read up quite easily. Here you two is. Okay. Well, if X is one, then why is gonna be too based on the top row? Why is to then, based on the second road, Zed is gonna be two times two is four. That's a second. I value that. Sorry. Second, I'm vector on Third Director would find in the same way. So a minus for I times you three. Yeah, close. They were Okay, So this matrix gonna be much for one 00 minus 41 eight minus 14. It was six. Minus seven minus four. Just three times by a factor. You three which were my ex wives, That because they were so that full again, we could just quite easy read off. What? The components of you three comm Bay. If the ex opponent is one in the white component, must be four. Based on the first row is that component must be 16 based on September. Okay, so therefore the fundamental matrix it's gonna be the first column is gonna be the first item Vector, which one won once was bye bye e to the the power of the first I can value, which was one times t. That's easy. It's the tea. It's the thing. Second column is gonna be Eat the two tea to ease the TT on for each of the TT for column is gonna be beat. The 40 for each of the 40 16 eats the 40. So that's the fundamental matrix to this matrix virtual body


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