Most Important Selected Qs for JEE AdvancedMathematicsMatrices
Match the following Column-I with Column-II
Options
- A( A ) ( r ) ;( B ) ( p ) ;( C ) ( q ) ;( D ) ( s )
- B( A ) ( s ) ;( B ) ( q ) ;( C ) ( r ) ;( D ) ( p )
- C( A ) ( q ) ;( B ) ( r ) ;( C ) ( s ) ;( D ) ( p )
- D( A ) ( q ) ;( B ) ( s ) ;( C ) ( r ) ;( D ) ( p )
Correct answer
C. ( A ) ( q ) ;( B ) ( r ) ;( C ) ( s ) ;( D ) ( p )
Step-by-step solution
(A) |A-x I|=0 There exists a non zero matrix X such that A X=x X aligned & |( Adj A) A| X=x( adj A) X & |A| I X=x( adj A) X & |A| X=x( adj A) X & |A| X x =( adj A) X & ( adj A) X= |A| X 2 aligned (B) | A ⁻- |=| (A- 1) |=| A- .1 | | A ^ - A |=0 if and only if | A- I |=0 | A - |=0 if and only if | A-i |=0 or is the root of | A ^ - xI |=0 if and only if is the root of |A-y I|=0 e ^ -1 is the required solution (C) |B- I|= [ array ccc |A₁₁ |- |A₁₂ | . . A_ 1 n 0 & |A₂₂ |- . . A_ 2 n 0 & 1 & 1 1 & 1 & 1 1 & 1 & 1 & 1 & |