Compute the determinant of following matrices A 1 0 1 2 1 1

Compute the determinant of following matrices A = (1 0 1 2 -1 1 5 -1 3) B = (4 6 2 3) Are these singular or nonsingular?

Solution

SOLUTION

Det A

= [1 x {( - 1 x 3) - (- 1 x 1)} - 0 x{(2 x 3) - (5 x 1)} + 1 x {(2 x -1) - (5 x 1)}]

= - 2 + 0 + 3 = 1 ANSWER

Det B = (4 x 3) - (2 x 6) = 12 - 12 = 0 ANSWER

CONCLUSION

Since det A is not equal to zero, it is NON-SINGULAR, but since det B is equal to zero, it is SINGULAR.