5

I3 1 1 U 8 3 0 1 338 4 W 0 1 8 0 1 8 Ji 3 1 1 1 8 1 8 V # Il83]7...

Question

I3 1 1 U 8 3 0 1 338 4 W 0 1 8 0 1 8 Ji 3 1 1 1 8 1 8 V # Il83]7

I3 1 1 U 8 3 0 1 338 4 W 0 1 8 0 1 8 Ji 3 1 1 1 8 1 8 V # Il 83] 7



Answers

$$ \left[\begin{array}{llll} 1 & 2 & 3 & 4 \\ 0 & 1 & 2 & 3 \\ 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 1 \end{array}\right] $$

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

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

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,


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