If the ranks of the matrices A= [ array ccc 1 & 0 & 1 2 & 1 & 2 1 & 0 & -1 array ] and B= [ array cccc 1 & 2 & 3 & 4 2 & 4 & 6 & -8 array ] are r₁ and r₂ respectively then r₁-r₂=

Step-by-step solution

A= [ array ccc 1 & 0 & 1 2 & 1 & 2 1 & 0 & -1 array ] | A |=1(-1-0)+1(0-1)=-1-1=-2=0 Rank of A ( r ₁ )=3 aligned & B = [ array cccc 1 & 2 & 3 & 4 2 & 4 & 6 & -8 array ] & | array cc 3 & 4 6 & -8 array |=-24-24=-48 0 aligned Rank of B (r₂ )=2 Now, r ₁- r ₂=3-2=1