Which of the following matrices are invertible? A = [ array cc 2 & 3 10 & 15 array ], B = [ array ccc 1 & 2 & 3 2 & -1 & 3 1 & 2 & 3 array ], C = [ array lll 1 & 2 & 3 3 & 4 & 5 4 & 6 & 8 array ], D = [ array lll 2 & 4 & 2 1 & 1 & 0 1 & 4 & 5 array ]

Step-by-step solution

aligned & |A|= [ array cc 2 & 3 10 & 15 array ]=30-30=0 & |B|= [ array ccc 1 & 2 & 3 2 & -1 & 3 1 & 2 & 3 array ]=0 [ R ₁ and R ₂ are identical ] & | C |= [ array lll 1 & 2 & 3 3 & 4 & 5 4 & 6 & 8 array ]=1(2)-2(4)+3(2)=0 & | D |= [ array lll 2 & 4 & 2 1 & 1 & 0 1 & 4 & 5 array ]=2(5)-4(5)+2(3)=-4 0 aligned