Determine the value of such that the matrix is the augmented matrix of a consistent linear system

Question

a) the matrix is the augmented matrix of a consistent linear system if h ≠ []

b) The matrix is the augmented matrix of a consistent linear system if h = []

c) The matrix is the augmented matrix of a consistent linear system for every value of h.

d) the matrix is not the augmented matrix of a consistent linear system for any value of h.

[]= need to fill in a value if chosen

Answer 1

If h = 4 then system inconsistent, because if h = 4 then raw operation R₂ + R₁(-5) → R₂ we get

|1 4 3|

|0 0 -3|

If h ≠ 4 system consistent.