Use cramers rule to 51 solve for xy and z x3y z1 2x yz2...

Transcript

00:01 Okay, so first system we're going to solve here.

00:03 We're going to use the kramer's rule.

00:05 Cravenor's rule is going to be depending on us finding our determinants for a variety of matrices.

00:11 So we're going to start with the coefficient matrix that's given here.

00:14 So i wrote this one down like that.

00:16 So next thing we're going to do is find the determinant of a.

00:20 Okay, so the determinant of a here is going to be basically we're taking one times the determinant of this little mini matrix.

00:28 And then we're going to be subtracting three.

00:30 Times this matrix determinant and then times negative one times this determinant.

00:37 So it's going to look like this.

00:39 It'll be one times this will be a negative two minus two times one is minus two.

00:46 And then we'll have minus three times it'll be four plus one and then minus one times four minus one.

00:59 And that comes out to a negative 22.

01:03 Okay, the next step is to do our, we're going to replace the x column here with our numbers here, 1, 2, negative 3.

01:12 So 1, 2, negative 3, and then everything else is going to stay the same.

01:17 So it'll be 3, negative 1, negative 1, 2, and 2.

01:21 So now i have to find this determinant.

01:24 So that's going to equal 2.

01:27 Sorry.

01:31 That's going to be 1 times a negative 2 minus 2 minus 3 times 4 plus 3 minus 1 times 4 minus 3 and that comes out to a negative 26.

01:43 Now we'll do the same thing with y.

01:45 So i'll have 1, 2, negative 1, 1, 2, 3 here.

01:51 And then negative 3, and then negative 1, 1, and 2.

01:55 So now this determinant is going to be 1 times 4 plus 3, minus 1 times 4 plus 1, minus 1 times a negative 6 plus 2, and that comes out to a positive 6.

02:08 And then finally we'll do this with z.

02:10 So we've got 1, 2, negative 3 here, and then the original numbers.

02:14 So it's going to be 1, 2, negative 1, 3, negative 1, 2.

02:19 And my determinant is going to look like 1 times 3 minus 4, minus 3 times a negative 6 plus 2, plus 1 times a 4 minus 1, and that equals 14...

Question

Use Cramer's rule to (5.1) Solve for x,y and z x,+3y,-z,=1 2x,-y,+z,=2 -x,+2y,+2z,=-3 (5.2) Solve for x and y (3)/(x)-(6)/(y)=(1)/(3) (2)/(x)+(3)/(y)=(1)/(2)

Question

Use Cramer's rule to (5.1) Solve for x,y and z x,+3y,-z,=1 2x,-y,+z,=2 -x,+2y,+2z,=-3 (5.2) Solve for x and y (3)/(x)-(6)/(y)=(1)/(3) (2)/(x)+(3)/(y)=(1)/(2)

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