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Cofactor expansion

Solve the first problem 12 problems

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1. Determinant of a 3×3 matrix ●○○○○ 10 ptsEvaluate the determinant of $\begin{pmatrix}2&1&1\\0&5&-2\\1&-3&4\end{pmatrix}$.
2. Determinant of a 3×3 matrix with entries 1 to 9 ●○○○○ 10 ptsEvaluate the determinant of $\begin{pmatrix}2&3&4\\5&6&7\\8&9&1\end{pmatrix}$.
3. Determinant by first-row cofactor expansion ●○○○○ 10 ptsCompute the determinant of $\left| \begin{array}{ccc}4&1&2\\4&0&3\\3&-2&5\end{array} \right|$ using a cofactor expansion across the first row.
4. Determinant of a 4x4 matrix ●●○○○ 20 ptsGiven $\begin{vmatrix} 2 & 2 & 3\\ x & y & z\\ a & 2b & 3c \end{vmatrix}=10$ with $x,y,z,a,b,c \in \mathbb{R}$, find $\begin{vmatrix} 0 & 3x & y & z\\ 0 & 3a & 2b & 3c\\ 0 & 6 & 2 & 3\\ 5 & 0 & 0 & 0 \end{vmatrix}$.
5. Determinant of a 3x3 matrix ●●○○○ 20 ptsFind the value of the determinant $\left|\begin{array}{ccc} 67 & 19 & 21 \\ 39 & 13 & 14 \\ 81 & 24 & 26 \end{array}\right|$.
6. Determinant of a 4×4 matrix ●●○○○ 20 ptsFind the determinant of the matrix $$A=\begin{pmatrix}1 & -1 & 0 & 2 \\ 3 & 1 & 4 & 1 \\ 0 & 0 & 1 & -3 \\ 1 & -1 & 0 & 4\end{pmatrix}.$$

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