Most Important Selected Qs for JEE AdvancedMathematicsMatrices
If A = ( a _ il )_ n n and f is a function defined as f ( A )= f ( a _ i ) _ n n . Let A == [ array cc 2 - & - & 2 - array ] Then
Options
- AA is invertible
- BA= A
- CA is orthogonal
- D(2 A)=2 A A
Correct answer
C. A is orthogonal
Step-by-step solution
A= [ array cc & - & array ] and A= [ array cc & & array ] | A|= ^2 + ^2 =1 Hence, A is invertible Also, ( A) ( A)^T= [ array cc & - & array ] [ array cc & - & array ]= [ array ll 1 & 0 0 & 1 array ]=1 Hence, A is orthogonal Also. 2 A A=2 [ array lr - & - & array ] [ array ll & & array ]=2 [ array ll 2 & 1 2 & 0 array ] 2 A