The solution set of left|begin{array}{ccc}x & | vedclass

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(B) Let the given determinant be $\Delta = \left|\begin{array}{ccc}x & 3 & 5 \ 2 & 6 & 10 \ 7 & 21 & 35\end{array}ight|$.Observe the columns of th

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$R$

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(B) Let the given determinant be $\Delta = \left|\begin{array}{ccc}x & 3 & 5 \ 2 & 6 & 10 \ 7 & 21 & 35\end{array}ight|$.Observe the columns of the determinant:Column $2$ is $C_2 = [3, 6, 21]^T$ and Column $3$ is $C_3 = [5, 10, 35]^T$.Notice that $C_3 = \frac{5}{3} C_2$.Since two columns are proportional,the value of the determinant is $0$ for any value of $x$.Alternatively,observe that row $2$ is $R_2 = [2, 6, 10]$ and row $3$ is $R_3 = [7, 21, 35]$.$R_3 = 3.5 	imes R_2$,which confirms the determinant is identically zero regardless of $x$.Thus,the equation holds for all real numbers $x \in R$.

The solution set of $\left|\begin{array}{ccc}x & 3 & 5 \\ 2 & 6 & 10 \\ 7 & 21 & 35\end{array}\right|=0$ is . . . . . . .

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