Practicing Success
The value of the determinant $\begin{vmatrix} a+1 & b & c \\a & b+1 & c \\a & b & c+1 \end{vmatrix} $ is : |
zero a+b+c a+b+c+1 abc+1 |
a+b+c+1 |
The correct answer is Option (3) → $a+b+c+1$ $Δ=\begin{vmatrix} a+1 & b & c \\a & b+1 & c \\a & b & c+1 \end{vmatrix}$ $C_1→C_1+C_2+C_3$ $Δ=\begin{vmatrix} a+b+c+1 & b & c \\a+b+c+1 & b+1 & c \\a+b+c+1 & b & c+1 \end{vmatrix}$ $Δ=(a+b+c+1)\begin{vmatrix} 1 & b & c \\1 & b+1 & c \\1 & b & c+1 \end{vmatrix}$ $R_2→R_2-R_1$ $R_3→R_3-R_1$ $Δ=(a+b+c+1)\begin{vmatrix} 1 & b & c \\0 & 1 & 0 \\0 & 0 & 1 \end{vmatrix}$ $Δ=a+b+c+1$ |