2. (a) Consider the following linear system of equations where k ∈R. x + y + z = 7 x + y −z = 5 −x −y + z = k (i) What v

[answerhappygod]

2. (a) Consider the following linear system of equations where k
∈R.
x + y + z = 7
x + y −z = 5
−x −y + z = k
(i) What value of k will give an infinite number of
solutions?
Justify your choice. [2 marks]
(ii) Using your value for k, form an augmented matrix, and reduce
it to reduced row
echelon form. [3 marks]
(iii) Using information from your matrix in (ii), produce the
vector equation of the line
along which all solutions will lie.