If the system of equations 2 x + 7 y + λ z = 3 3 x + 2 y + 5 z = 4 x + μ y + 32 z = − 1 has infinitely many solutions, then ( λ − μ ) is equal to________

Question

If the system of equations ​ 2 x + 7 y + λ z = 3 3 x + 2 y + 5 z = 4 x + μ y + 32 z = − 1 ​ has infinitely many solutions, then ( λ − μ ) is equal to________

TestHub · Accepted Answer

​ D = D 1 ​ = D 2 ​ = D 3 ​ = 0 D 3 ​ = ​ 2 3 1 ​ 7 2 μ ​ 3 4 − 1 ​ ​ = 0 ⇒ μ = − 39 D = ​ 2 3 1 ​ 7 2 − 39 ​ λ 5 32 ​ ​ = 0 ⇒ λ = − 1 λ − μ = 38 ​

Mathematics - Determinant Question with Solution | TestHub

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