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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
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Solution
Let, A = `[(1,1,1),(2,3,2),(a,a,2a)]`, X = `[(x),(y),(z)]`, B = `[(1),(2),(4)]`
|A| = `|(1,1,1),(2,3,2),(a,a,2a)|`
= 1 × (3 × 2a − a × 2) − 1 × (2 × 2a − a × 2) + 1 × (2 × a − a × 3)
= 4a − 2a − a
= a ≠ 0
Hence, the system of equations is consistent.
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