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Question
Examine the consistency of the system of equations.
x + y + z = 1
2x + 3y + 2z = 2
ax + ay + 2az = 4
Solution
Let, `A = [(1,1,1),(2,3,2),(a,a,2a)], X = [(x),(y),(z)], B = [(1),(2),(4)]`
`abs A = [(1,1,1),(2,3,2),(a,a,2a)]`
`= 1 xx (3 xx 2a - a xx 2) - 1 xx (2 xx 2a - a xx 2) + 1 xx (2 xx a - a xx 3)`
= 4a - 2a - a
`= a ne 0`
a ≠ 0 and the system of equations is consistent.
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