Question

Investigate the values of λ and µ the system of linear equations 2x + 3y + 5z = 9, 7x + 3y – 5z = 8, 2x + 3y + λz = µ, have no solution

Answer 1

Martix form `[(2, 3, 5),(7, 3, -5),(2, 3, lambda)][(x),(y),(z)] = [(0),(8), (mu)]`

AX = B

[A|B] = `[(2, 3, 5, |, 9),(7, 3, -5, |, 8),(2, 3, lambda, |, mu)]`

`{:("R"_2 -> 2"R"_2 - 7"R"_1),("R"_3 -> "R"_3 - "R"_1),(->):} [(2, 3, 5, |, 9),(0, -15, -45, |, -47),(0, 0, lambda - 5, |, mu - 90)]`

Case:

If λ = 5

µ ≠ 9

ρ(A) = 2

ρ(A|B) = 3

ρ(A) ≠ ρ(A|B)

The system is inconsistent.

It has no solution.