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Singular and Non Singualar Matrices

Calculate the...

Question

Calculate the values of the determinants:
$∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} 7 & 13 & 10 & 6 5 & 9 & 7 & 4 8 & 12 & 11 & 7 4 & 10 & 6 & 3 \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣$ .

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Solution

$\Rightarrow Δ = ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} 7 & 13 & 10 & 6 5 & 9 & 7 & 4 8 & 12 & 11 & 7 4 & 10 & 6 & 3 \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ C_{1} = C_{1} + C_{2} - {2 C}_{3} \Rightarrow Δ = ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} 0 & 13 & 10 & 6 0 & 9 & 7 & 4 0 & 12 & 11 & 7 0 & 10 & 6 & 3 \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣$
All the elements of one column of the determinant are zero
$\Rightarrow Δ = 0$

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