# Using matrices, solve the following system of linear equations : x + 2y − 3z = −4 2x + 3y + 2z = 2 3x − 3y − 4z = 11 - Mathematics

Sum

Using matrices, solve the following system of linear equations :

x + 2y − 3z = −4
2x + 3y + 2z = 2
3x − 3y − 4z = 11

#### Solution

The system of equations can be written in the form AX = B, where

A = [(1,2,-3),(2,3,2),(3,-3,-4)], X=[("x"),("y"),("z")] and B =[(-4),(2),(11)]

|A| = 1 (-12+6) - 2 (-8 - 6) - 3 (-6 - 9) = 67 ≠ 0

Therefore, A is non singular and so its inverse exists.

A11 = -6, A12 = 14, A13 = -15

A21 = 17, A22 = 5, A23 = 9

A31 = 13, A32 = -8, A33 = -1

Therefore, "A"^-1 = 1/67[(-6,17,13),(14,5,-8),(-15,9,-1)]

So X = A-1 B =1/67[(-6,17,13),(14,5,-8),(-15,9,-1)][(-4),(2),(11)]

i.e. [("x"),("y"),("z")]=1/67[(201),(-134),(67)]=[(3),(-2),(1)]

Hence, x = 3, y = -2 and z = 1

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