Question

If A is the coefficient matrix of the above system of equations and

, then the elements of
are
, the elements of
are
, and the elements
are
. The solution of this system is (x, y, z) =

Answer 1

Explanation:

Coefficient matrix A of size 3 * 3 is =

[ 1 1 0 ]

[ 2 0 -1 ]

[ 0 1 -3 ]

Let the matrix B of size 3 * 1 be

[ 10 ]

[ 9 ]

[ -5 ]

Let's first find the determinant of A.

Row 1 - Row3 =>

[1 0 3 ]

[2 0 -1 ]

[0 1 -3].

R2 - 2 R1 =>

[1 0 3 ]

[0 0 -7]

[0 1 -3]

Divide Row2 by -7.

[1 0 3]

[0 0 1] * -7

[0 1 -3].

Interchange R2 and R3.

[1 0 3]

[0 1 -3]

[0 0 1] * -7.

R1 - 3 * R3 gives us

[1 0 0]

[0 1 -3]

[0 0 1] * -7

R2 + 3* R3 gives us

[1 0 0 ]

[0 1 0 ]

[0 0 1] * -7.

So the determinant of A = -7.

Inverse of A = A^-1 = -1/7 * cofactor matrix =

[ -2 6 2 ]

[ 3 -3 -1 ] * -(1/7)

[ -1 1 -2 ]

So R1 = [-2 6 2]. R2 = [-3 3 1]. R3 = [-1 1 -2].

For finding the solution of the system of equations given, perform the same operations on the column matrix B as were done on the matrix A to reduce it to the identity matrix. B =

[ 162/7]

[ -92/7 ]

[ -19/7 ].

The solution is x = 162/7, y = -92/7, and z = -19/7.