Answer :

A =

Let B = A^{T} =

|B| =

= ( – 1 – 8) – 0 – 2( – 8 + 3) = – 9 + 10 = 1

Cofactors of B are:

C_{11} = – 9 C_{21} = 8 C_{31} = – 5

C_{12} = – 8 C_{22} = 7 C_{32} = – 4

C_{13} = – 2 C_{23} = 2 C_{33} = – 1

adj B =

=

So, adj B =

Now, B ^{– 1} =

Hence, (A^{T}) ^{– 1}

Rate this question :

Which of the following statements are True or False

If A, B and C are square matrices of same order, then AB = AC always implies that B = C.

Mathematics - ExemplarWhich of the following statements are True or False

If A, B and C are square matrices of same order, then AB = AC always implies that B = C.

Mathematics - ExemplarUsing matrices solve the following system of equations.

3x + 4y + 7z = 4

2x – y + 3z = –3

x + 2y – 3z = 8

Mathematics - Board PapersUsing matrices, solve the following system of equations:

2x - 3y + 5z = 11

3x + 2y - 4z = -5

x + y - 2z = -3

Mathematics - Board PapersUsing matrices solve the following system of equations:

x + y – z = 3; 2x + 3y + z = 10; 3x – y – 7z = 1

Mathematics - Board PapersIf A is an invertible matrix and A^{-1} = then A=?

If A=is not invertible then λ=?

RS Aggarwal - MathematicsFind the adjoint of the matrix and hence show that A(adj A) = |A| I_{3}.