A – 4A = – I A A (A – ) – A A – = – I A – (Post multiplying by A – because |A| ≠ ) A (A A – ) – 4I = – A – AI – 4I = – A – A – = 4I – A = Hence = EXERCISE . Find adjoint of each of the matrices in Exercises and . . .
Verify A ( adj A) = ( adj A) A = |A| I in Exercises and . . Find the inverse of each of the matrices (if it exists) given in Exercises to . .
. . DETERMINANTS . .
Verify that (AB) – = B – A – . . If A = , show that A – 5A + 7I = O. Hence find A – .
. For the matrix A = , find the numbers a and b such that A + a A + b I = O. . For the matrix A = Show that A – 6A + 5A + I = O.
Hence, find A – . . If A = Verify that A – 6A + 9A – 4I = O and hence find A – . Let A be a nonsingular square matrix of order × .
Then | adj A| is equal to (A) | A | (B) | A | (C) | A | (D) |A| . If A is an invertible matrix of order , then det (A – ) is equal to (A) det (A) (B) det (A) (C) (D) . Applications of Determinants and Matrices In this section, we shall discuss application of determinants and matrices for solving the system of linear equations in two or three variables and for checking the consistency of the system of linear equations. Consistent system A system of equations