Evaluate det A and detAt Compare detA and detAT for a A 4 2

Evaluate det (A) and det(A^t). Compare det(A) and det(A^T) for: (a) A = [4 -2 -3 3]; (b)A = [-3 -1 2 5 -3 6 1 0 4]

Solution

a) A = [ 4 -2

-3 3 ]

det A = (4x3) - (-2 x-3) = 12-6 = 6

A^T = [ 4 -3

-2 3 ]

det (A^T) = (4x3) - (-3x-2) = 12-6 = 6

Therefore,

det A = det (A^T)

b)

det (A) = -3(-3 x4- 6x0 ) -(-1) (5x4 -6x1) + 2 [5x0 - (-3x1)]

= 36 +14 +6

= 56

A^T = [ -3 5 1

-1 -3 0

2 6 4]

det(A^T) = -3 (-3x 4 - 6x0) - 5 (-1x4 - 2x0) +1 [-1x6-(-3x2)]

= 36 + 20

= 56

Therefore,

det A = det (A^T)