Question

How to solve for A,B,C, and D given the following equations:

A+C=0
B-D=0
4A+3D+2C=7
A+4B+6C=-6

Answer 1

you would start by solving one of the eqn for any variable, and then plug that information in to a different eqn and solve that for a different var until you eventually have numerical interpretations for the vars.

Answer 2

once you have more than 2 variables, I would use elimination.

write all equations, with the variables sorted alphabetical
in fact, we can leave out the "names" and just write the coefficients

Answer 3

A+C=0 1 0 1 0 | 0
B-D=0 0 1 0 -1 | 0
4A+3D+2C=7 4 0 2 3 | 7
A+4B+6C=-6 1 4 6 0 | -6

Answer 4

oh this is something i can solve with a matrix?

Answer 5

yes, now use "elimination"

to zero out the first column (if you know how to do that)

Answer 6

example: multiply the 1st row by -4 and add to the 3rd row to get a new 3rd row

Answer 7

then multiply the 1st row by -1 and add to the 4th row to get a new 4th row

Answer 8

you should get
1 0 1 0 | 0
0 1 0 -1 | 0
0 0 -2 3 | 7
0 4 5 0 | -6

Answer 9

now zero out the 2nd column below the 2nd row
only 1 step: multiply the 2nd row by -4 and add to the 4th row to get a new 4th row

Answer 10

Well i don't know how to do it on paper but my teacher showed us how to do it on calculator using the matrix and rref so i did it that way. are the answers A=2, B=1, C=-2, and D=1 ?

Answer 11

yes, you want to find reduced row, echelon form
If you got the correct answer, those values will work in the original equations

Answer 12

ok. Thanks for the help!

Answer 13

yw