Question

Use Cramer's rule to solve the system. 2x + 4y - z = 32 x - 2y + 2z = -5 5x + y + z = 20

A. {( 1, -9, -6)}

B. {( 2, 7, 6)}

C. {( 9, 6, 9)}

D. {( 1, 9, 6)}

Answer 1

@ganeshie8

Answer 2

It's multiple choice so does it matter how you solve it? To me Cramer's rule would be too slow to solve a basic problem like that.

Answer 3

Still good to know how to do it. For Ax=b, Cramer's rule states that \[x _{i}=\det(A _{i)}/\det(A)\] where Ai is the matrix formed by replacing the ith column with b.

Answer 4

Not seeing a way to show a 3x3 matrix with the equation tools. Let me think how to show this.. lol

Answer 5

It's the bottom selection in the Equation tool. Bottom left option.

Answer 6

That's a 2x2 unless there's an option to change that somewhere.

Answer 7

\[\left[\begin{matrix}1 & 2 & 5 \\ 3 & 4 & 6 \\ 7 & 8 & 9 \end{matrix}\right]\]
1 & 2 & 5 \\ 3 & 4 & 6 \\ 7 & 8 & 9

Answer 8

\\ for extra row and & for extra columns

Answer 9

Ah thanks so much.

Answer 10

Pleasure. Go for it lol. I did Cramer's rule last semester but I'm a bit rusty. Will have to review it again.

Answer 11

Take the determinant of:\[\left[\begin{matrix}32 & 4 & -1\\ -5 & -2 & 2\\20 & 1 & 1 \end{matrix}\right]\]to find the solution for x. Insert the b column matrix into the 2nd column for y and the 3rd for z. As Mandre said though, typically you don't want to do this for 3x3 matrices as it is time consuming. Especially when you have high entries like 32 and 20 lol.

Answer 12

i dont get it at all. im sorry

Answer 13

Do you know how to take the determinant of a 3x3 matrix?

Answer 14

nope

Answer 15

Have you ever computed curl of two 3 dimensional vectors?

Answer 16

Not curl. Cross product. Sorry wrong term.

Answer 17

ive done cross product if your talking like multiplication

Answer 18

As in the vector operation. Sometimes called outer product. Probably not but that's similar. Um ok let me find an explanation and link it.

Answer 19

okay

Answer 20

http://en.wikipedia.org/wiki/Determinant scroll down to 3x3 matrices.

Answer 21

alright makes sense thats alot lol

Answer 22

Yeah it's kind of a lot of work once you get above 2x2 or 3x3 which is why you'd probably use software lol. But the principle is nice to know.

Answer 23

okay well can you show me how to solve this so i know for sure

Answer 24

Okay I'm using Wolfram Alpha to solve the determinants so I can save some time. I'm going to solve all four of the ones we'll use and then you can do that on your own for practice if you want. XD

Answer 25

thats fine..

Answer 26

\[\left[\begin{matrix}32 & 4 & -1 \\ -5 & -2 & 2\\ 20 & 1 & 1\end{matrix}\right]\] Okay the determinant of this is 17. I may walk you through of the determinants just so you can see it but it's just a lot of calculations to do 4 of them.

Answer 27

And that one is A1 btw. I should label these.

Answer 28

dont even worry about it maybe another day

Answer 29

Are you sure?

Answer 30

yea

Answer 31

Ok good luck with it.

Answer 32

The answer is D anyhow.