Diketahui [tex] \left[\begin{array}{ccc}p-1&p\\1-q&q\\\end{array}\right] [/tex] matriks singular. Jika p dan q memenuhi persamaan 2x^2 + x - a = 0 maka nilai a

jawab

matriks singular Det = 0
q(p-1) - p(1- q)  = 0
pq - q - p + pq = 0
2pq = p + q ...(i)

2x² + x - a = 0
p + q  = -1/2 ...(ii)
p q = - a/2...(iii)

(ii dan iii) substitusikan ke (i)

2pq = p + q
2(-a/2) = - 1/2
- a  = - 1/2
a= 1/2

Matriks Singular

determinan = 0

2x² + x - a = 0
p + q = -b/a = -1/2
p . q = c/a = -a/2

det = 0
q(p - 1) - p(1 - q) = 0
pq - q - p + pq = 0
2pq - (p + q) = 0
2(-a/2) - (-1/2) = 0
-a + 1/2 = 0
a = 1/2