If A is a matrix such that [ array ll 2 & 1 3 & 2 array ] A [ array ll 1 & 1 array ]= [ array ll 1 & 1 0 & 0 array ] then A is equal to

Step-by-step solution

Let aligned & A= [ array l x₁ x₂ array ] & [ array ll 2 & 1 3 & 2 array ] [ array l x₁ x₂ array ] [ array ll 1 & 1 array ] &= [ array c 2 x₁+x₂ 3 x₁+2 x₂ array ] [ array ll 1 & 1 array ] &= [ array cc 2 x₁+x₂ & 2 x₁+x₂ 3 x₁+2 x₂ & 3 x₁+2 x₂ array ] aligned aligned & [ array cc 2 x₁+x₂ & 2 x₁+x₂ 3 x₁+2 x₂ & 3 x₁+2 x₂ array ]= [ array ll 1 & 1 0 & 0 array ] & 2 x₁+x₂=1 and 3 x₁+2 x₂=0 aligned On solving, we get aligned & & x₁=2 and & & x₂=-3 & & A= [ array r 2 -3 array ] aligned