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Kendrick Hampton

Kendrick Hampton

Answered question

2022-06-22

need to find four variables, a , b , c , d , , and I have four equations:
1) u 1 a v 1 b + c = u 1
2) u 1 b v 1 a + d = v 1
3) u 2 a v 2 b + c = u 2
4) u 2 b v 2 a + d = v 2
Note that u 1 , v 1 , u 1 , v 1 , u 2 , v 2 , u 2 , v 2 are all known.
Any suggestions to how to solve for the four variables, a , b , c , d?

Answer & Explanation

Schetterai

Schetterai

Beginner2022-06-23Added 25 answers

Four equations, four unknowns: a , b , c , d .
1) u 1 a v 1 b + c = u 1
2) u 1 b v 1 a + d = v 1
3) u 2 a v 2 b + c = u 2
4) u 2 b v 2 a + d = v 2
Try subtracting row 3 from row 1 (the "c's" cancel out):
5) ( u 1 u 2 ) a ( v 1 v 2 ) b = ( u 1 u 2 )
Subtracting row 4 from row 2 (the "d's" cancel out):
6) ( u 1 u 2 ) b ( v 1 v 2 ) a = ( v 1 v 2 )
Rearranging 6):
6) ( v 2 v 1 ) a + ( u 1 u 2 ) b = ( v 1 v 2 )
Now you're down to two equations (5, 6') in two unknowns!

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