The augmented matrix for Au0 is Find and equation that a and

The augmented matrix for Au=0 is Find and equation that a and b must satisfy so that Au=0 will have non-trivial solutions.

Solution

given non trivial solutions

so determinant of A is not equal to zero

so |A| = 5 (ab - a^2* 5) -3(0*b - 0*a^2) +1 (0*-5 - a*0)

   |A| = 5(ab -5a^2) -3(0) +1(0)

|A| = (5ab -25a^2) +0

5ab -25a^2 0

5a (b - 5a) 0

so a 0 and b 5a