Answer:
k = 13
Step-by-step explanation:
Matrix is;
A =
[2 -5 9]
[-1 3 -5]
[ 7 1 k ]
Number of unknowns is less than the rank of 2. Thus, the determinant has to be zero for us to find k.
Thus, we have;
2((3 × k) - (-5 × 1)) -(-5)((-1 × k) - (-5 × 7)) + 9((-1 × 1) - (7 × 3)) = 0
Simplifying further gives;
2(3k +5) + 5(-k + 35) + 9(-22) = 0
6k + 10 - 5k + 175 - 198 = 0
k - 198 + 185 = 0
k - 13 = 0
k = 13
