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in Applications of Matrices and Determinants by (46.9k points)
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Find k if the equations x + y + z = 3; x + 3y + 2z = 6; x + 5y + 3z = k are inconsistent.

1 Answer

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by (47.6k points)
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Best answer

Given that the system is inconsistent

For the equations to be inconsistent, ρ[(A, B)] ≠ ρ(A) 

Here ρ(A) = 2 So ρ([A, B]) ≠ 2 

That is the last row of the echelon matrix should not be zero

⇒ k ≠ 9

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