the system of linear equations below has a unique solution for all but one value of a:
9x−18y=36
22x+ay=88
What is this exceptional value for a?
i got a=-44y/y but its wrong, please explain how to do and what i did wrong
2006-10-19 15:31:29 · 5 answers · asked by Diggler AKA The Cab Driver 1 in Science & Mathematics ➔ Mathematics
the solution is trivial when the two systems are LD (dependant)
9 -18
22 a ...........(reduction... divide top by 9 ... bottom by 22)
1 -2
1 a/22 ............(a/22 must be = to -2) -44
your answer is correct .... without the y/y term
the columns of the matrix are the coefficents of the variable ..
"A" is in the "Y" col .... so it is the coefficent of y
2006-10-19 15:39:29 · answer #1 · answered by Brian D 5 · 0⤊ 1⤋
Let M be the following matrix:
[9, -18]
[22, a]
Your system of equations has a unique solution if and only if det(M)≠0. So to find the exception, find the value of a for which det (M)=0. We have:
9a+18*22=0
a+44=0
a=-44
The reason you got the answer wrong is because the y/y term is unnecessary - whether the system of equations has a unique solution does not depend on the fact that y is nonzero (note that if y is nonzero, the y/y term cancels, yielding simply a=-44, whereas if y=0, your solution is undefined, whereas the system of equations still has multiple solutions).
2006-10-19 15:46:21 · answer #2 · answered by Pascal 7 · 1⤊ 0⤋
your system is singular if tyhe determinant = 0
9a + 22*18 = 0 <=> a = -44
2006-10-19 20:26:15 · answer #3 · answered by gjmb1960 7 · 0⤊ 0⤋
$6000 borrowed at 7.8% APR over 36 months could artwork out to a cost of $188.03. that would recommend the finished you will pay for the internal maximum loan could be $6769.08, subsequently you will pay $769.08 in interest on the internal maximum loan.
2016-10-02 11:49:42 · answer #4 · answered by ? 4 · 0⤊ 0⤋
a = (88-22x)/y
a has no solution if y=0 (cos a will be infinity, therefore unacceptable solution)
I think, I'm not sure though
2006-10-19 15:40:20 · answer #5 · answered by Anonymous · 0⤊ 0⤋