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Find the determinant of the following matrix.

2  2  4  2

3  0  5  0

0  2  0  2

0  2  0  5

 Jun 13, 2021
 #1
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Find the determinant of the following matrix.

\(\begin{pmatrix} 2 & 2 & 4 & 2 \\ 3 & 0 & 5 & 0 \\ 0 & 2 & 0 & 2 \\ 0 & 2 & 0 & 5 \\ \end{pmatrix}\)

 

\(\begin{array}{|rcll|} \hline \begin{vmatrix} 2 & 2 & 4 & 2 \\ 3 & 0 & 5 & 0 \\ 0 & 2 & 0 & 2 \\ 0 & 2 & 0 & 5 \\ \end{vmatrix} &=&2* \begin{vmatrix} 0 & 5 & 0 \\ 2 & 0 & 2 \\ 2 & 0 & 5 \\ \end{vmatrix} -3* \begin{vmatrix} 2 & 4 & 2 \\ 2 & 0 & 2 \\ 2 & 0 & 5 \\ \end{vmatrix} \\ &=&2*(-5)* \begin{vmatrix} 2 & 2 \\ 2 & 5 \\ \end{vmatrix} -3*(-4)* \begin{vmatrix} 2 & 2 \\ 2 & 5 \\ \end{vmatrix} \\ &=&(-10+12)* \begin{vmatrix} 2 & 2 \\ 2 & 5 \\ \end{vmatrix} \\ &=&2* \begin{vmatrix} 2 & 2 \\ 2 & 5 \\ \end{vmatrix} \\ &=&2*(2*5-2*2) \\ &=&2*(10-4) \\ &=&2*6 \\ &=& \mathbf{12} \\ \hline \end{array}\)

 

laugh

 Jun 13, 2021

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