SOLUTION: Hi, I asked a question on this set of equations a little while ago, but was wondering, could one use Cramers Rule to solve the following .. a*4 + b*2 + c*9 + d * 7 = 21 a* 2 +

Algebra ->  Algebra  -> Matrices-and-determiminant -> SOLUTION: Hi, I asked a question on this set of equations a little while ago, but was wondering, could one use Cramers Rule to solve the following .. a*4 + b*2 + c*9 + d * 7 = 21 a* 2 +       Log On

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Question 4221: Hi, I asked a question on this set of equations a little while ago, but was wondering, could one use Cramers Rule to solve the following ..
a*4 + b*2 + c*9 + d * 7 = 21
a* 2 + b*5 + c*4 + d*4 = 11.5
a*6 + b*3 + c*5 + d*3 = 15.5
a * 8 + b * 4 + c * 6 + d * 6 = 22
If so, I would be most grateful if someone could show me how ... or get me started anyway :)
And could a general 'formula' be created using this rule to solve other similar sets of equations?
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
are your terms all powers? or is a*4 really 4a etc?

if they are coefficients then:

matrix%285%2C4%2C+4%2C2%2C9%2C7%2C21%2C+2%2C5%2C5%2C4%2C11.5%2C+6%2C3%2C5%2C3%2C15.5%2C+8%2C4%2C6%2C6%2C22%29

Now, the trouble is working out a 4x4 determinant. I do not have the time to walk though or type this here, so i advise you look on the web for a step-by-step guide to 4x4 matrices.

Anyway, Cramer's rule - ideal for this question.

work out the determinant, D for matrix%284%2C4%2C+4%2C2%2C9%2C7%2C+2%2C5%2C5%2C4%2C+6%2C3%2C5%2C3%2C+8%2C4%2C6%2C6%29

then work out the determinant, Da for matrix%284%2C4%2C+21%2C2%2C9%2C7%2C+11.5%2C5%2C5%2C4%2C+15.5%2C3%2C5%2C3%2C+22%2C4%2C6%2C6%29

Then do the same for Db, Dc and Dd -->

matrix%284%2C4%2C+4%2C21%2C9%2C7%2C+2%2C11.5%2C5%2C4%2C+6%2C15.5%2C5%2C3%2C+8%2C22%2C6%2C6%29
matrix%284%2C4%2C+4%2C2%2C21%2C7%2C+2%2C5%2C11.5%2C4%2C+6%2C3%2C15.5%2C3%2C+8%2C4%2C22%2C6%29
matrix%284%2C4%2C+4%2C2%2C9%2C21%2C+2%2C5%2C5%2C11.5%2C+6%2C3%2C5%2C15.5%2C+8%2C4%2C6%2C22%29

If you are still sane, then:

a = Da/D
b = Db/D
c = Dc/D
d = Dd/D

jon