5

3 4 0 4 1 9 % H 2 9 1 8 6 E C € E % € 1 # t 3 V36 1 t 1 1 } { 6 L 0 0 8 1 1 ! 3 8 [...

Question

3 4 0 4 1 9 % H 2 9 1 8 6 E C € E % € 1 # t 3 V36 1 t 1 1 } { 6 L 0 0 8 1 1 ! 3 8 [

3 4 0 4 1 9 % H 2 9 1 8 6 E C € E % € 1 # t 3 V36 1 t 1 1 } { 6 L 0 0 8 1 1 ! 3 8 [



Answers

Subtract. $$ \left(\frac{3}{8} t^{9}-\frac{1}{10} t^{3}-\frac{13}{4} t\right)-\left(\frac{1}{8} t^{9}-\frac{1}{2} t^{3}-\frac{5}{4} t\right) $$

Rescued are preserved new magics iss made by either x t and I, which means e So we first write downs, air magics, ex key in the left and we write our three come stree magics are in the right. If one fear of the our old Sarah was the arrow, they're a 01 Cem we simple So retract it three times the versatile wrong second road and they're subtracted nine times in the first arose from They're so thorough you So when new magics were looks like please. Well, minors streaky say our own act till night Look to 90 and, uh, wealthy arrow zero negative story with Carol back to marry 01 fan we add is a fucking the rolf run three times in the first row and the super tractor three times in the second row Drawn the further rolled. So the new magics were looks like 34 Sorry, sorry. Sorry. Holmes. So a keep our theory Row one c r o neg took three when miners three t 003 and the hero was the arrow knocked history were in general p r o negative three want and ah, as added the several choose three times the first rule and add a win. Miners of three top three tee times off a thorough to three times the filler. The second row. So the new magics were Looks like faithful in you don't like it Took nine year old They're off their own actives free and fair. A 01 not you. Not known t four minus 33 Our own detective story in the world. Then less multiply the first row by went over in our own times He's very t pulver So second and rolled by Not everyone went overnight. And the soda robe I worked never went over three. So the new magics were looks like these with euro 0010001 And if they are all the arrow we're over night Any negative history piece Power run naked tea free tea liners were over night. They are a one negative. We're over three. So So answer will be these parts. Whose answer? Yes. Okay, So pardon It's your problem. Weren't Dr T Sorry key minus one over nine year old word. Negative. We're over three

So in this problem we're given this five x 5 matrix And were asked to use a matrix calculator, luckily in order to determine or find the determinant. All right, because you can do this by hand. I might be a little difficult. You can probably pick Grow four here and you know avoid two of the calculations. But then you're gonna still be left with four x 4 Matrix sees and working those ways where's goes down. So this can be a lot quicker. So we go over here to the new matrix. In our matrix calculator. We went to Desmond's dot com math tools matrix calculator to get this. And our matrix is a five by five. I gotta get this thing built up here, the framework of it five by five. and so the first entry is a three and then a minus two A four three. You know, one, Then a 1-0 -1 zero 2102 on Euro. And then 5 -15. My ass. One 032 zero three, two Than 4 7 -8. 4 seven. Mine it's eight and zero zero. And then we have 123 one two three 02 zero two chris Sanders. So that's all in there. Now I need the determinant of this Five by five. So I go d et determinant of A And there it is 410. That was a lot quicker and a lot easier. And trying to do this all out my hand, wasn't it

In this question we have to use row reduction to find the inverse is of the given batteries if they exist. And check it by multiplication. No, let us consider the metrics. Yeah. 123, 4 01, 2, 3 0012 0001. And on the right side identity metrics. Or for the four 1000 0100 0010 0001. Now we will row reduce the all metrics. We will apply the operation are funny those two our than minus two. Our two stores too, uh minus Artie And our three stores too. Our 3 -R4. On applying these operations, we get the metrics 1111. Yeah 01 11 00 11 little little 01. And on the right hand side we get 1 -10 needle 01 minus one deedle needle needle one minus one 0001. Again. We will apply the operation are one stores too, Urban -R2. Our two stores too, Our 2- Artery. And our three stores too. Our three minus are full on applying these operations to get the metrics 1000 0100 0010 0001. And on the right hand side one minus two, one needle 0 1 -2, one digital hell one minus two 0001. So in investment taxes, one minus two, one hero 01 minus 21 001 -2 0001. Yeah. Now we will check it by multiplication. We will multiply A. And N. Was matrix. So we can write a Multiplied by a invest metrics equals two 1234 0123 beetle beetle 12 0001. Multiplied by in west metrics 1 -210 0 1 -2 one. You know the middle one by understood deedle deedle? They're all one. No. Yeah all multiplication. We will first multiplied by stroke with first column. So one multiplied by one plus two multiplied by zero Plus three multiplied by zero Plus four, multiplied by zero On simplifying it we get one similarly. Now we will multiply first row by second column one multiplied by -2 plus two, multiplied by one, three multiplied by zero Plus four, multiplied by zero and simplifying it. Be good feel Now we will write these values in the desire my tricks, €1. By following a similar method we will find the other elements of the metrics. So you know beetle 0100 0010 0001. Hence hey multiplied by and was metrics. It were to identity matrix. Thank you

Okay, This problem, we have equals to falling. And it's also a three by tweet matrix. So we have negative. 310 and then zero negative. 31 and four Negative. Eight two. Now we can obtain the characteristic equation again. As follows. The same exact procedure as the previous problems. We have a negative Lambda cute minus four. Lambda squared minus five. Lambda minus two equals zero. So, Landau, one comma to come on three are gonna equal native one negative one. And negative, too. Now, for Lambda equals negative too. We want to solve the following equation for the Eiken victor. A plus two i times u equals zero. Then we'll obtain u equals T where Ty's every parameter, as always, times 111 And for Lambda equals negative one. We saw this equation a plus. I times you equal zero. And when we solve this, we will get you is equal to a T times 1/2 1 and two or equivalently team times one, two and four. Because this is just the Eiken victor skilled differently, scaled up. And so we have our answers


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