EXERCISE . . Solve the following system of homogenous equations. (i) (ii) .
Determine the values of λ for which the following system of equations has (i) a unique solution (ii) a non-trivial solution. . By using Gaussian elimination method, balance the chemical reaction equation: C H O H O CO - - EXERCISE . Choose the Correct or the most suitable answer from the given four alternatives : .
If | ) | | adj(adj A , then the order of the square matrix A is ( ) ( ) ( ) ( ) . If A is a × non-singular matrix such that AA A A T T and B A A T − , then BB T = ( ) A ( ) B ( ) I ( ) B T . If A = , B = adj and C = , then | adj B C ( ) ( ) ( ) ( ) . If A = , then A = ( ) ( ) ( ) ( ) .
If A = , then I ( ) A − ( ) A − ( ) A − ( ) A − . If A = and B = then | ) | adj AB = ( ) − ( ) − ( ) − ( ) − . If P is the adjoint of × matrix A and | A = , then x is ( ) ( ) ( ) ( ) . If A = and A − = then the value of a is ( ) ( ) − ( ) − ( ) − .
If A B and C are invertible matrices of some order, then which one of the following is not true? ( ) adj A A A ( ) adj adj adj )( AB B ( ) det