Solve each of the following systems of equations by...

Solve each of the following systems of equations by converting to a matrix equation and using the inverse of the coefficient matrix. 3x-6y+z=6 -x+y-z=-7 x-2y= 1 Note: Use desmos the find the inverse of the 3x3matrix. x=? y=? z=?

Transcript

00:02 I'm going to find the solution to the systems of equation using the inverse coefficient matrix.

00:08 So our equations are x plus y plus z equals negative 1.

00:14 Then no x here plus 1 plus plus y plus 3z equals negative 5.

00:24 And then x we have no y plus z should be an x here equals negative 2.

00:33 So we're solving this by the inverse matrix.

00:35 So what we're going to do is we're going to make a matrix out of our x, y, and z coefficients.

00:40 So we have 1 .01, 1, 1 ,0, 131.

00:49 And then out of our constant, so we have negative 1, negative 5, negative 2.

00:54 So this is our a and this is our b.

00:58 We're trying to figure out what a inverse is.

01:02 So first we have to do is we have to find the determinant of this one right here.

01:11 So first to find the determinant, one, and then we're going to do this matrix right here.

01:21 So 1, and then 1 .031, minus the second one, 0131, plus the third one, 0110.

01:35 Okay, so calculate this, i get 1 times 1 minus 0, minus 1, minus 3, and then 1 times 0 minus 3.

01:49 So when i calculate that out, i get 3.

01:53 So my determinant is going to be 3.

01:57 To find our inverse matrix, so we have to do 1 over the determinant of our a times our adjacent matrix of a.

02:06 So we're going to find that adjacent matrix.

02:08 So what we're going to do is you're going to rewrite our matrix.

02:13 1 -1 -0 -1 -3 -101.

02:17 So we know that this is column 1, column 2.

02:20 We're going to repeat column 1 and column 2.

02:25 So 1 -1 -1 -0.

02:30 And then this is row 1 and this is row 2.

02:33 We're going to repeat row 2 and 1 -1 at the bottom.

02:36 So 1 -1 -1 -1 -1 -0 -0 -0.

02:39 3 .01.

02:41 Now we're going to erase this first row and this first column.

02:47 So what we're going to do is we're going to find determinants of each of the matrices, and i'll show you what that looks like in a second.

03:00 So i'm going to make a column of matrices right here.

03:03 What we're going to do is i'm going to find the determinants going up like this.

03:09 So i do 1 times 1 minus 3 times 0, which is just 1.

03:16 It's going to go right here.

03:17 Then i'm going to go down.

03:19 So 1 times 0 minus 1 is negative 1...

Question

Solve each of the following systems of equations by converting to a matrix equation and using the inverse of the coefficient matrix. 3x-6y+z=6 -x+y-z=-7 x-2y= 1 Note: Use desmos the find the inverse of the 3x3﻿matrix. x=? y=? z=?

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Solve each of the following systems of equations by converting to a matrix equation and using the inverse of the coefficient matrix. 3x-6y+z=6 -x+y-z=-7 x-2y= 1 Note: Use desmos the find the inverse of the 3x3matrix. x=? y=? z=?