The following system of linear equations
2x + 3y + 2z = 9
3x + 2y + 2z = 9
x $-$ y + 4z = 8
Solution
$$\Delta = \left| {\matrix{
2 & 3 & 2 \cr
3 & 2 & 2 \cr
1 & { - 1} & 4 \cr
} } \right| = - 20 \ne 0$$ $\therefore$ unique solution<br><br>$${\Delta _x} = \left| {\matrix{
9 & 3 & 2 \cr
9 & 2 & 2 \cr
8 & { - 1} & 4 \cr
} } \right| = 0$$<br><br>$${\Delta _y} = \left| {\matrix{
2 & 9 & 2 \cr
3 & 9 & 2 \cr
1 & 8 & 4 \cr
} } \right| = - 20$$<br><br>$${\Delta _z} = \left| {\matrix{
2 & 3 & 9 \cr
3 & 2 & 9 \cr
1 & { - 1} & 8 \cr
} } \right| = - 40$$<br><br>$\therefore$ $x = {{{\Delta _x}} \over \Delta } = 0$<br><br>$y = {{{\Delta _y}} \over \Delta } = 1$<br><br>$z = {{{\Delta _z}} \over \Delta } = 2$<br><br>Unique solution : (0, 1, 2)
About this question
Subject: Mathematics · Chapter: Matrices and Determinants · Topic: Types of Matrices and Operations
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