Question #8784

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

Expert's answer

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).

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).

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