If the following system of linear equations
2x + y + z = 5
x $-$ y + z = 3
x + y + az = b
has no solution, then :
Solution
Here $$D = \left| {\matrix{
2 & 1 & 1 \cr
1 & { - 1} & 1 \cr
1 & 1 & a \cr
} } \right|\matrix{
{ = 2(a - 1) - 1(a - 1) + 1 + 1} \cr
{ = 1 - 3a} \cr
} $$<br><br>$${D_3} = \left| {\matrix{
2 & 1 & 5 \cr
1 & { - 1} & 3 \cr
1 & 1 & b \cr
} } \right|\matrix{
{ = 2( - b - 3) - 1(b - 3) + 5(1 + 1)} \cr
{ = 7 - 3b} \cr
} $$<br><br>for $a = {1 \over 3},b \ne {7 \over 3}$, system has no solutions.
About this question
Subject: Mathematics · Chapter: Matrices and Determinants · Topic: Types of Matrices and Operations
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