Find the value for k for which the matrix?

Question

Find the value for k for which the matrix
A=
-3 -6 -18
2 -9 -14
-8 3 k
has rank 2.
K=

Answer 1

what do you know about rank?

Answer 2

the matrix will have rank 2 if only 2 rows (or columns) are linearly independent, so solve

-3x - 6y = -18
2x - 9y = -14

x + 2y = 6
2x + 4y = 12
-2x + 9y = 14
13y = 26
y = 2

x + 2(2) = 6
x = 2

then
-8(2) + 3(2) = k
-16 + 6 = k
k = -10