COMEDK2018MathematicsMatrices
If [ array cc 1 & - & 1 array ] [ array cc 1 & - & 1 array ]= [ array cc a & -b b & a array ] then
Options
- Aa=1=b
- Ba= 2 , b= 2
- Ca= 2 , b= 2
- Da= , b=
Correct answer
B. a= 2 , b= 2
Step-by-step solution
We have, [ array cc 1 & - & 1 array ]⁻¹= 1 1+ ² [ array cc 1 & - & 1 array ] [ [ array ll a & b c & d array ]⁻¹= 1 a d-b c [ array cc d & -b -c & a array ] ] Now, [ array cc 1 & - & 1 array ] [ array cc 1 & - & 1 array ]⁻¹= [ array cc a & -b b & a array ] [ array cc 1 & - & 1 array ] ( 1 1+ ² ) [ array cc 1 & - & 1 array ]= [ array cc a & -b b & a array ] 1 1+ ² [ array cc 1- ² & -2 2 & 1- ² array ]= [ array cc a & -b b & a array ] [ array cc 2 & - 2 2 & 2 array ]= [ array cc a & -b b & a array ] a= 2 , b= 2