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8 8 8R6 867 8 # 11 W 1 7 1 2 3 zh 6"...

Question

8 8 8R6 867 8 # 11 W 1 7 1 2 3 zh 6"

8 8 8R6 867 8 # 11 W 1 7 1 2 3 zh 6"



Answers

11. $$-3,2,-\frac{4}{3}, \frac{8}{9},-\frac{16}{27}, \dots$$

You're going to be subtracting these fractions. Ah We're going to start by trying to find the number, The lowest number that can be divided by 8, 5, 2 and 10. And that number will be 40. So we will make all of our denominators 40. So we have to look at what we multiply by each of our denominators In order to get 40. And in the case of eight we take eight times five to get 40. So therefore we need to take five times 5 to give us our new numerator of 25. five times 8 is 40 two times a gives us 16, two times 20 is 40 three times 20, gives us 60 10 times four is 40 And 11 times four gives us 44. So um when we subtract a negative will really be adding. So we can think of us as having a plus here, the negative 25 plus 16. Well give us -9 over 40 And then 60 -44 will give us 16. So the negative 9 -16 Gives us -25 Over 40. Now we're not quite done yet, Because both 25 and 40 Can divide by five, so our answer further simplifies into negative 5/8.

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.

So in this problem, we're given this matrix and were asked to use the matrix capability of a graphing utility to find the determinant. So I went to Desmond's dot com, went up here to math tools, matrix calculator, and got this matrix calculator here. So in our new matrix and our matrix is a four by four. So four rose and four columns. Now the entries one minus one, C A A and four and two and six zero my S four and then to zero two and six and then zero two, eight zero. Okay, where's my matrix now? Just do D E T right here to get the determinant determinant of a yes, Negative,

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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