DeterminantHard
Question
The system of linear equations x + y - z = 6, x + 2y - 3z = 14 and 2x + 5y - λz = 9 (λ ∈ R) has a unique solution if
Options
A.λ = 8
B.λ = 8
C.λ = 7
D.λ ≠ 7
Solution
Here ᐃ = 
system has unique solution if ᐃ ≠ 0 and at least one of ᐃx, ᐃy, ᐃz is non-zero.
ᐃ = 1(-2λ + 15) - 1(- λ + 6) - 1(5 - 4) ≠ 0 ⇒ - 2λ + 15 +λl - 6 - 1 ≠ 0
⇒ - l + 8 ≠ 0 ⇒ λ ≠ 8
system has unique solution if ᐃ ≠ 0 and at least one of ᐃx, ᐃy, ᐃz is non-zero.ᐃ = 1(-2λ + 15) - 1(- λ + 6) - 1(5 - 4) ≠ 0 ⇒ - 2λ + 15 +λl - 6 - 1 ≠ 0
⇒ - l + 8 ≠ 0 ⇒ λ ≠ 8
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