Find all t such that t4 2 3 t90t1 3 4 t20 Solutiona detA 0 o

Find all t such that |t-4 2 3 t-9|=0|t-1 3 4 t-2|=0

Solution

a) detA =0   of given matrix:

determinant of A : (t-4)(t- 9) - 6 =0

t^2 - 13t +36 =0

Use quadratice formula to solve equation : t = ( 13 + / - sqrt( 13^2 - 4*36) )/2

=( 13 + /- 5 )/2

t = 28/2 = 14

t = 8/2 = 4

Solution : t= 4 , 14

b) detA =0

(t-1)(t-2) -12 =0

t^2 -3t +2 -12 =0

t^2 -3t -10 =0

Solve the above quadratic equation to get values of t

t^2 -5t +2t -10 =0

t( t -5) +2( t-5) =0

(t+2)(t-5) =0

t = -2 and t=5

Solution : t = -2 , 5