The set of equations 𝑥 + 𝑦 + 𝑧 = 1 𝑎𝑥 – 𝑎𝑦 + 3𝑧 = 5

Q. The set of equations

𝑥 + 𝑦 + 𝑧 = 1

𝑎𝑥 – 𝑎𝑦 + 3𝑧 = 5

5𝑥 − 3𝑦 + 𝑎𝑧 = 6

has infinite solutions, if a =

(A) −3

(B) 3

(C) 4

(D) −4

Sol:

ρ(A)=ρ(AB)< no.of variables
|A|=0