5

8 8 8 1 1 2 1 0 i 1& 31 3 1 0 ] 31 73...

Question

8 8 8 1 1 2 1 0 i 1& 31 3 1 0 ] 31 73

8 8 8 1 1 2 1 0 i 1 & 3 1 3 1 0 ] 3 1 7 3



Answers

$\left[ \begin{array}{rrr}{-3} & {1} & {0} \\ {0} & {-3} & {1} \\ {4} & {-8} & {2}\end{array}\right]$

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,

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


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