Find all values of lambda for which the following determinan

Find all values of lambda for which the following determinant will equal 0: lambda =

Solution

Determinant D = (1 - )(3 - ) - 2(2)

==> D = 3 - - 3 + ² -4

==> D = ² - 4 -1

Determinant = 0

==> D = 0

==> ² - 4 -1 = 0

==> ² - 2(2) + 2² - 2² -1 = 0

==> ( - 2)² - 5 = 0

==> ( - 2)² = 5

==> - 2 = 5 , -5

==> = 2 - 5 , 2 + 5

==> = -0.23607 , 4.2361

Hence for = -0.23607 , 4.2361 , the determinant = 0