Which of the following determinants have value 'zero'? 1. | array...

1. $\begin{aligned} \left|\begin{array}{lll} 41 & 1 & 5 \\ 79 & 7 & 9 \\ 29 & 5 & 3 \end{array}\right| & =\left|\begin{array}{lll} 40 & 1 & 5 \\ 72 & 7 & 9 \\ 24 & 5 & 3 \end{array}\right| C_1 \rightarrow C_1-C_2 \\ & =8\left|\begin{array}{lll} 5 & 1 & 5 \\ 9 & 7 & 9 \\ 3 & 5 & 3 \end{array}\right|=0 \end{aligned}$$\because$ two columns are same so value of determinant is zero. 2. $\begin{aligned} \left|\begin{array}{lll} 1 & a & b+c \\ 1 & b & c+a \\ 1 & c & a+b \end{array}\right| & =\left|\begin{array}{lll} 1 & a+b+c & b+c \\ 1 & a+b+c & c+a \\ 1 & a+b+c & a+b \end{array}\right| \quad C_2 \rightarrow C_2+C_3 \\ & =(a+b+c)\left|\begin{array}{lll} 1 & 1 & b+c \\ 1 & 1 & c+a \\ 1 & 1 & a+b \end{array}\right|=0 \end{aligned}$$\because$ two columns are same so value of determinant is zero. 3. \left|$\begin{array}{ccc}0 & c & b \\ -c & 0 & a \\ -b & -a & 0\end{array}$\right|=0\because diagonal is zero so value of determinant is zero.