5

03=78i [ 8 L { 3 3 8 1 8 {1 1 1 3 3 3 8 8 1 8 2 1 8 38 5...

Question

03=78i [ 8 L { 3 3 8 1 8 {1 1 1 3 3 3 8 8 1 8 2 1 8 38 5

03=7 8i [ 8 L { 3 3 8 1 8 { 1 1 1 3 3 3 8 8 1 8 2 1 8 3 8 5



Answers

$$ \frac{8 y-4}{5 y+2}-6 $$

From the given equation. I just multiply eight on both sides, so the question becomes two y minus three. Holy square plus y is equal toe. Why minus five Holy Square plus six. Going ahead and solving it. So I get four y square minus two worldwide plus nine plus y is equal toe y square plus 25 minus stand. Why minus six. So solving it I get the final equation is three by square minus Y minus. 10 is equal to zero Now. I will just desperate the middle term, so just look at it carefully. I can write. The value is three by square, minus six way plus five y minus. Stand is equal to zero, going ahead and solving it further so I can take three wide common. So I get why minus two and taking five common from here. So I get why minus two is equal to zero so I can write the values. Why managed to multiplication three y plus five is equal to zero. No solving it further. So I get why you managed to is equal to zero or three y plus five is equal to zero. So we get why physical toe to or y is equal to minus five by three, which is our solutions

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

It's this problems institutes attract to pound on meals. We have negative for Y square minus three wide plus a There were some trying to I square minus six line minus two. The truth of subtraction is to distribute that negative into our second parentheses. So we changed it to a plus. We can change this to a negative to a positive six line than a positive too. So our final answer will be negative for plus negative too. So be negative. Six y square. You have negative three plus six plus three y. Then we have positive eight plus two, which is less 10. So our final polynomial will be negative. Six y squared plus three y plus 10. Thank you very much.

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.


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