Answer to Question #8784 in Linear Algebra for Omoregbe Frank

Question

1 Solve the set of linear equations by the matrix method: a+3b+2c=3, 2a-b-3c= -8, 5a+2b+c=9. Solve for a

(A) 2
(B) 4
(C) 7
(D) 3

Answer 1

Let's write down the matrix of the given system:

1 & 3 & 2& | 3
2 -1 -3& |& -8
5 & 2 & 1& | 9

Now let's transform it to the unit matrix:

1 & 3 & 2& | 3
0 -7 -7& | -14
0 -13 -9& |& -6


1 & 3 & 2& | 3
0 & 1 & 1& | 2
0 -13 -9& |& -6

1 & 0 -1& |& -3
0 & 1 & 1& | 2
0 & 0 & 4& |& 20

1 & 0 -1& |& -3
0 & 1 & 1& | 2
0 & 0 & 1& | 5

1 & 0 & 0& | 2
0 & 1 & 0& |& -3
0 & 0 & 1& | 5

So, a = 2, b = -3, c = 5. The right answer is (A).