For what value of k, the matrix A = \(\left[\matrix{k+5&6\\-1&k}\right]\) will be singular?
Answer & explanation
Correct answer: option 3
\( { k }^{ 2 } +5k+6 =0\)
k2 + 2k + 3k + 6 = 0
(k2 + 2k) + (3k + 6) = 0
k(k+2) + 3(k+2) = 0
(k+2) (k+3) = 0
k+2 = 0 or k+3 = 0
k = -2 or k = -3