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Matrices

3 by 3 Determinant

         

If matrices \( A \) and \( B \) are given as follows, what is \( \text{det}\left( AB \right) ? \) \[A = \begin{pmatrix} 3 & 5 & 4 \\3 & 6 & 5 \\ 3 & 4 & 9 \end{pmatrix} \quad B = \begin{pmatrix} 4 & -4 & 8 \\8 & -7 & 16 \\ 2 & -1 & 5 \end{pmatrix} \]

Find the determinant of the following matrix: \[ A = \begin{pmatrix} 2 & 5 & 2 \\2 & 6 & 3 \\ 2 & 4 & 8 \end{pmatrix}. \]

Find the determinant of the following matrix: \[ A = \begin{pmatrix} 2 & 1 & 0 \\5 & 3 & 5 \\ 2 & 1 & 0 \end{pmatrix}. \]

Find the determinant of the following matrix: \[ A = \begin{pmatrix} 3 & 1 & 0 \\6 & 6 & 4 \\ 1 & 1 & 1 \end{pmatrix}. \]

If matrices \( A \) and \( B \) are given as follows, what is \( \text{det}\left( AB \right) ? \) \[A = \begin{pmatrix} 2 & 6 & 6 \\2 & 7 & 3 \\ 5 & 5 & 7 \end{pmatrix} \quad B = \begin{pmatrix} 2 & 1 & 2 \\2 & 2 & 5 \\ 2 & 1 & 2 \end{pmatrix} \]

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