The cofactors of the elements of the first column of the matrix $A=\left[\begin{array}{ccc}2 & 0 & -1 \\ 3 &…

The cofactors of the elements of the first column of the matrix $A=\left[\begin{array}{ccc}2 & 0 & -1 \\ 3 & 1 & 2 \\ -1 & 1 & 2\end{array}\right]$ are
  1. $0,-7,2$
  2. $0,-1,1$
  3. $0,-8,4$
  4. $-1,3,-2$

Solution

We know, $\begin{array}{l} C_{i j}=(-1)^{i+j} \times M_{i j} \\ C_{11}=(-1)^{111} \times\left|\begin{array}{ll} 1 & 2 \\ 1 & 2 \end{array}\right|=(-1)^{2} \times 0=0 \\ C_{21}=(-1)^{2+1} \times\left|\begin{array}{cc} 0 & -1 \\ 1 & 2 \end{array}\right|=(-1)^{3} \times(1)=-1 \\ C_{31}=(-1)^{3+1} \times\left|\begin{array}{cc} 0 & -1 \\ 1 & 2 \end{array}\right|=(-1)^{4} \times(1)=1 \end{array}$

Asked in: MHT CET 2020 (19 Oct Shift 2)

Practice more Matrices questions on Aicharya