Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT2022MathematicsMatricesActual

Let A= [ array ccc 1 & -1 & 1 2 & 1 & -3 1 & 1 & 1 array ] and 10 B= [ array ccc 4 & 2 & 2 -5 & 0 & 1 & -2 & 3 array ] If B is the inverse of A , then the value of is

Options

  1. A4
  2. B3
  3. C-4
  4. D5

Correct answer

D. 5

Step-by-step solution

A= [ array ccc 1 & -1 & 1 2 & 1 & -3 1 & 1 & 1 array ] |A|= [ array ccc 1 & -1 & 1 2 & 1 & -3 1 & 1 & 1 array ]=1(1+3)+1(2+3)+1(2-1)=4+5+1=10 Adj A= [ array ccc 4 & -5 & 1 2 & 0 & -2 2 & 5 & 3 array ]^T= [ array ccc 4 & 2 & 2 -5 & 0 & 5 1 & -2 & 3 array ] B=A⁻¹= 1 10 [ array ccc 4 & 2 & 2 -5 & 0 & 5 1 & -2 & 3 array ] [ A⁻¹= 1 |A| Adj A ] 10 B= [ array ccc 4 & 2 & 2 -5 & 0 & 5 1 & -2 & 3 array ] Hence, =5

Practice Matrices on Quantrex Academy →

More from Matrices

If A= 1 3 [ array ccc 1 & 2 & 2 2 & 1 & -2 a & 2 & b array ] is an orthogonal matrix, then 2024If matrix A= [ array ccc 3 & -2 & 4 1 & 2 & -1 0 & 1 & 1 array ] and A⁻¹= 1 k adj (A) , then k is 2024If A and B are symmetric matrices of same order such that A B+B A=X and A B-B A=Y , then (X Y)^ T = 2024If A= [ array cc 1 & 0 0 & -1 array ], P= [ array ll 1 & 1 0 & 1 array ] and X=A P A^T , then A^T X⁵⁰ A= 2024If A is a square matrix of order 3 , then Adj ( Adj .A^2 ) = 2024If A= [ array ccc 0 & c & -b -c & 0 & a b & -a & 0 array ] and B= [ array ccc a^2 & a b & a c a b & b^2 & b c a c & b c & c^2 array ] , then A B is equal to 2023If A = [ array cc 0 & 2 3 & -4 array ] and k ~A = [ array cc 0 & 3 a 2 b & 24 array ] , then the values of k, a and b respectively are: 2023If [ array cc 1 & - & 1 array ] [ array cc 1 & - & 1 array ]⁻¹= [ array cc a & -b b & a array ], then 2022 Full Matrices list All BITSAT PYQs