Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -2 & 3 & 0 & 5 \\ -6 & 1 & 6 & 1 \\ 3 & 0 & 0 & -1 \\ -5 & 6 & 4 & -3 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -2 & 3 & 0 & 5 \\ -6 & 1 & 6 & 1 \\ 3 & 0 & 0 & -1 \\ -5 & 6 & 4 & -3 \end{array}\right] = -632 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -1 & 1 & 2 & -1 \\ 4 & -1 & -3 & 6 \\ 0 & 0 & 1 & -2 \\ -3 & -3 & 5 & 1 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -1 & 1 & 2 & -1 \\ 4 & -1 & -3 & 6 \\ 0 & 0 & 1 & -2 \\ -3 & -3 & 5 & 1 \end{array}\right] = -78 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -2 & 6 & 2 & -5 \\ -1 & -6 & 0 & -3 \\ -5 & 5 & 0 & -3 \\ -4 & 0 & 1 & 3 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -2 & 6 & 2 & -5 \\ -1 & -6 & 0 & -3 \\ -5 & 5 & 0 & -3 \\ -4 & 0 & 1 & 3 \end{array}\right] = -655 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -3 & 4 & 2 & -2 \\ 6 & -6 & -2 & 0 \\ 0 & 0 & 3 & -1 \\ -6 & 3 & 6 & 4 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -3 & 4 & 2 & -2 \\ 6 & -6 & -2 & 0 \\ 0 & 0 & 3 & -1 \\ -6 & 3 & 6 & 4 \end{array}\right] = -6 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} 2 & 6 & -5 & 1 \\ 0 & -2 & -4 & 0 \\ 3 & 6 & 2 & -3 \\ 1 & -4 & -1 & 0 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} 2 & 6 & -5 & 1 \\ 0 & -2 & -4 & 0 \\ 3 & 6 & 2 & -3 \\ 1 & -4 & -1 & 0 \end{array}\right] = -248 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} 2 & 5 & 0 & -4 \\ 3 & -3 & 6 & 4 \\ 4 & 3 & -5 & -6 \\ -1 & 0 & 0 & -3 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} 2 & 5 & 0 & -4 \\ 3 & -3 & 6 & 4 \\ 4 & 3 & -5 & -6 \\ -1 & 0 & 0 & -3 \end{array}\right] = -635 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -3 & -2 & -4 & 0 \\ 1 & 0 & 3 & 0 \\ -2 & -4 & -1 & 1 \\ 4 & 5 & 5 & 4 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -3 & -2 & -4 & 0 \\ 1 & 0 & 3 & 0 \\ -2 & -4 & -1 & 1 \\ 4 & 5 & 5 & 4 \end{array}\right] = -51 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} 6 & 0 & 1 & -1 \\ 4 & -1 & -6 & 0 \\ -4 & -2 & -5 & 3 \\ 3 & -4 & -3 & 0 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} 6 & 0 & 1 & -1 \\ 4 & -1 & -6 & 0 \\ -4 & -2 & -5 & 3 \\ 3 & -4 & -3 & 0 \end{array}\right] = 256 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -1 & -1 & 4 & 0 \\ 1 & -1 & -4 & 3 \\ 6 & 6 & 0 & 1 \\ -2 & 1 & 1 & 0 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -1 & -1 & 4 & 0 \\ 1 & -1 & -4 & 3 \\ 6 & 6 & 0 & 1 \\ -2 & 1 & 1 & 0 \end{array}\right] = 230 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} 1 & -4 & -2 & 0 \\ 2 & 3 & 5 & -2 \\ -3 & -5 & 3 & 5 \\ 0 & 1 & 3 & 0 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} 1 & -4 & -2 & 0 \\ 2 & 3 & 5 & -2 \\ -3 & -5 & 3 & 5 \\ 0 & 1 & 3 & 0 \end{array}\right] = -24 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -5 & -6 & -6 & -6 \\ -3 & -1 & 0 & 0 \\ 2 & 2 & 5 & 2 \\ 2 & -5 & 0 & -1 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -5 & -6 & -6 & -6 \\ -3 & -1 & 0 & 0 \\ 2 & 2 & 5 & 2 \\ 2 & -5 & 0 & -1 \end{array}\right] = -265 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -5 & 5 & -2 & -1 \\ -1 & 0 & 0 & 0 \\ 5 & 4 & 5 & 5 \\ 4 & 3 & 6 & 1 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -5 & 5 & -2 & -1 \\ -1 & 0 & 0 & 0 \\ 5 & 4 & 5 & 5 \\ 4 & 3 & 6 & 1 \end{array}\right] = -156 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} 6 & -1 & -6 & -1 \\ 3 & 6 & 6 & 0 \\ -5 & 2 & -4 & 3 \\ -4 & 1 & 2 & 0 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} 6 & -1 & -6 & -1 \\ 3 & 6 & 6 & 0 \\ -5 & 2 & -4 & 3 \\ -4 & 1 & 2 & 0 \end{array}\right] = 486 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} 1 & -3 & -3 & -2 \\ -2 & 2 & 0 & -1 \\ 1 & -4 & 0 & -6 \\ 1 & 2 & 0 & -3 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} 1 & -3 & -3 & -2 \\ -2 & 2 & 0 & -1 \\ 1 & -4 & 0 & -6 \\ 1 & 2 & 0 & -3 \end{array}\right] = 180 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} 3 & 2 & 3 & 0 \\ -4 & 2 & -6 & 1 \\ 4 & -4 & 5 & -2 \\ 6 & -1 & 6 & 0 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} 3 & 2 & 3 & 0 \\ -4 & 2 & -6 & 1 \\ 4 & -4 & 5 & -2 \\ 6 & -1 & 6 & 0 \end{array}\right] = -45 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} 0 & -3 & -6 & 5 \\ -1 & 1 & -6 & 3 \\ 0 & 2 & 1 & 0 \\ 6 & 2 & 1 & -1 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} 0 & -3 & -6 & 5 \\ -1 & 1 & -6 & 3 \\ 0 & 2 & 1 & 0 \\ 6 & 2 & 1 & -1 \end{array}\right] = -237 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -4 & -6 & 4 & 0 \\ 6 & 5 & 5 & 0 \\ 1 & 0 & 5 & -1 \\ -6 & -2 & 1 & 2 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -4 & -6 & 4 & 0 \\ 6 & 5 & 5 & 0 \\ 1 & 0 & 5 & -1 \\ -6 & -2 & 1 & 2 \end{array}\right] = 288 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} 3 & 1 & 0 & 1 \\ 1 & 2 & 1 & 0 \\ -4 & -1 & -2 & 6 \\ -2 & 2 & 0 & -2 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} 3 & 1 & 0 & 1 \\ 1 & 2 & 1 & 0 \\ -4 & -1 & -2 & 6 \\ -2 & 2 & 0 & -2 \end{array}\right] = 68 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -2 & 0 & -4 & 2 \\ 2 & -1 & -6 & -6 \\ -4 & 0 & -4 & 4 \\ -2 & -2 & 4 & -3 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -2 & 0 & -4 & 2 \\ 2 & -1 & -6 & -6 \\ -4 & 0 & -4 & 4 \\ -2 & -2 & 4 & -3 \end{array}\right] = 24 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} 1 & 1 & -1 & 2 \\ 0 & 0 & -1 & -3 \\ 2 & -6 & -4 & 3 \\ 5 & -5 & 2 & 0 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} 1 & 1 & -1 & 2 \\ 0 & 0 & -1 & -3 \\ 2 & -6 & -4 & 3 \\ 5 & -5 & 2 & 0 \end{array}\right] = 298 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -4 & 3 & 2 & 6 \\ -1 & 0 & -1 & -3 \\ 5 & 0 & 5 & -1 \\ 6 & 0 & 3 & -5 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -4 & 3 & 2 & 6 \\ -1 & 0 & -1 & -3 \\ 5 & 0 & 5 & -1 \\ 6 & 0 & 3 & -5 \end{array}\right] = -144 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -1 & 6 & 0 & 1 \\ -1 & 0 & -3 & 0 \\ 6 & -1 & -3 & -3 \\ -2 & -3 & -2 & 3 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -1 & 6 & 0 & 1 \\ -1 & 0 & -3 & 0 \\ 6 & -1 & -3 & -3 \\ -2 & -3 & -2 & 3 \end{array}\right] = -337 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -6 & -4 & 4 & -5 \\ -1 & -6 & -1 & 6 \\ 4 & -2 & 0 & 2 \\ 0 & 0 & 2 & 1 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -6 & -4 & 4 & -5 \\ -1 & -6 & -1 & 6 \\ 4 & -2 & 0 & 2 \\ 0 & 0 & 2 & 1 \end{array}\right] = 600 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -4 & -3 & 0 & -5 \\ 1 & 1 & -2 & -3 \\ -5 & -6 & 0 & 6 \\ 3 & -6 & 0 & 5 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -4 & -3 & 0 & -5 \\ 1 & 1 & -2 & -3 \\ -5 & -6 & 0 & 6 \\ 3 & -6 & 0 & 5 \end{array}\right] = -786 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -4 & 5 & 4 & -5 \\ -3 & -4 & 2 & 5 \\ -2 & 5 & 3 & 2 \\ 1 & 0 & 3 & 0 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -4 & 5 & 4 & -5 \\ -3 & -4 & 2 & 5 \\ -2 & 5 & 3 & 2 \\ 1 & 0 & 3 & 0 \end{array}\right] = -868 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} 0 & 0 & 4 & -5 \\ 4 & 3 & 3 & 2 \\ -3 & 0 & -4 & 6 \\ 5 & 1 & 6 & 5 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} 0 & 0 & 4 & -5 \\ 4 & 3 & 3 & 2 \\ -3 & 0 & -4 & 6 \\ 5 & 1 & 6 & 5 \end{array}\right] = 425 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -3 & 6 & -4 & 3 \\ -4 & 6 & 1 & -1 \\ 1 & 0 & -3 & 0 \\ 6 & -3 & -2 & 0 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -3 & 6 & -4 & 3 \\ -4 & 6 & 1 & -1 \\ 1 & 0 & -3 & 0 \\ 6 & -3 & -2 & 0 \end{array}\right] = 246 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} 4 & 2 & -6 & -3 \\ -2 & 3 & -5 & -1 \\ -1 & -6 & 1 & -5 \\ 0 & -3 & 0 & 1 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} 4 & 2 & -6 & -3 \\ -2 & 3 & -5 & -1 \\ -1 & -6 & 1 & -5 \\ 0 & -3 & 0 & 1 \end{array}\right] = -721 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -3 & -4 & 2 & -3 \\ 4 & -3 & 2 & -2 \\ 1 & 3 & 0 & 0 \\ 4 & -3 & 0 & -2 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -3 & -4 & 2 & -3 \\ 4 & -3 & 2 & -2 \\ 1 & 3 & 0 & 0 \\ 4 & -3 & 0 & -2 \end{array}\right] = -110 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -5 & 2 & -1 & 1 \\ -4 & 1 & 0 & -4 \\ 3 & 2 & 0 & 4 \\ 0 & 5 & -3 & 2 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -5 & 2 & -1 & 1 \\ -4 & 1 & 0 & -4 \\ 3 & 2 & 0 & 4 \\ 0 & 5 & -3 & 2 \end{array}\right] = -187 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} 0 & 2 & 0 & -5 \\ -2 & 2 & -2 & 4 \\ -4 & 2 & 0 & 5 \\ -1 & -3 & 1 & 4 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} 0 & 2 & 0 & -5 \\ -2 & 2 & -2 & 4 \\ -4 & 2 & 0 & 5 \\ -1 & -3 & 1 & 4 \end{array}\right] = -64 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} 3 & 4 & 0 & 4 \\ -3 & 3 & 1 & -1 \\ 4 & 0 & 0 & -3 \\ -6 & -4 & 2 & -4 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} 3 & 4 & 0 & 4 \\ -3 & 3 & 1 & -1 \\ 4 & 0 & 0 & -3 \\ -6 & -4 & 2 & -4 \end{array}\right] = 218 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} 4 & -6 & -2 & 4 \\ -3 & -3 & -5 & -4 \\ 6 & -3 & -6 & 0 \\ 0 & 2 & 1 & 0 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} 4 & -6 & -2 & 4 \\ -3 & -3 & -5 & -4 \\ 6 & -3 & -6 & 0 \\ 0 & 2 & 1 & 0 \end{array}\right] = 84 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -2 & -1 & 0 & -1 \\ 4 & -1 & 2 & -2 \\ -1 & 0 & 3 & 0 \\ 2 & 6 & -1 & 2 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -2 & -1 & 0 & -1 \\ 4 & -1 & 2 & -2 \\ -1 & 0 & 3 & 0 \\ 2 & 6 & -1 & 2 \end{array}\right] = -111 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} 6 & 1 & -2 & 1 \\ 0 & 3 & 1 & 0 \\ -1 & -6 & -6 & -2 \\ 5 & -6 & 1 & 2 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} 6 & 1 & -2 & 1 \\ 0 & 3 & 1 & 0 \\ -1 & -6 & -6 & -2 \\ 5 & -6 & 1 & 2 \end{array}\right] = 71 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} 5 & 4 & 6 & 5 \\ -6 & -6 & 4 & -6 \\ 3 & 2 & 0 & 6 \\ 0 & -2 & 0 & 1 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} 5 & 4 & 6 & 5 \\ -6 & -6 & 4 & -6 \\ 3 & 2 & 0 & 6 \\ 0 & -2 & 0 & 1 \end{array}\right] = -292 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} 2 & 6 & 2 & -2 \\ -1 & 5 & 0 & 1 \\ 1 & -1 & 6 & -5 \\ 0 & -2 & 1 & 0 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} 2 & 6 & 2 & -2 \\ -1 & 5 & 0 & 1 \\ 1 & -1 & 6 & -5 \\ 0 & -2 & 1 & 0 \end{array}\right] = 80 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -3 & 4 & 0 & -6 \\ 4 & -3 & 0 & 1 \\ -1 & 3 & 3 & 6 \\ 3 & 2 & 1 & 2 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -3 & 4 & 0 & -6 \\ 4 & -3 & 0 & 1 \\ -1 & 3 & 3 & 6 \\ 3 & 2 & 1 & 2 \end{array}\right] = -203 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -4 & 0 & 0 & 4 \\ -4 & -2 & -1 & -6 \\ -3 & 1 & 2 & 4 \\ 6 & 0 & 5 & -4 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -4 & 0 & 0 & 4 \\ -4 & -2 & -1 & -6 \\ -3 & 1 & 2 & 4 \\ 6 & 0 & 5 & -4 \end{array}\right] = 184 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -3 & -5 & -1 & 3 \\ 3 & -3 & 4 & 3 \\ 6 & 0 & -3 & -2 \\ 0 & -2 & -1 & 0 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -3 & -5 & -1 & 3 \\ 3 & -3 & 4 & 3 \\ 6 & 0 & -3 & -2 \\ 0 & -2 & -1 & 0 \end{array}\right] = 168 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} 6 & -3 & -2 & -3 \\ 6 & -5 & -1 & 4 \\ 3 & 4 & 0 & -5 \\ -2 & 4 & 0 & 6 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} 6 & -3 & -2 & -3 \\ 6 & -5 & -1 & 4 \\ 3 & 4 & 0 & -5 \\ -2 & 4 & 0 & 6 \end{array}\right] = -540 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} 3 & 0 & 4 & -3 \\ -2 & -6 & -2 & -6 \\ 1 & 0 & 3 & 0 \\ 5 & -6 & 1 & 1 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} 3 & 0 & 4 & -3 \\ -2 & -6 & -2 & -6 \\ 1 & 0 & 3 & 0 \\ 5 & -6 & 1 & 1 \end{array}\right] = -534 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -1 & -3 & 1 & -5 \\ -3 & 6 & -4 & 6 \\ 5 & 3 & -4 & -4 \\ 0 & -1 & -3 & 0 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -1 & -3 & 1 & -5 \\ -3 & 6 & -4 & 6 \\ 5 & 3 & -4 & -4 \\ 0 & -1 & -3 & 0 \end{array}\right] = 731 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} 5 & -1 & 0 & -4 \\ -3 & 2 & 1 & -6 \\ 0 & 5 & 0 & 2 \\ 6 & 5 & 2 & -3 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} 5 & -1 & 0 & -4 \\ -3 & 2 & 1 & -6 \\ 0 & 5 & 0 & 2 \\ 6 & 5 & 2 & -3 \end{array}\right] = -431 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -3 & 1 & 4 & -4 \\ 3 & -5 & 3 & -5 \\ 0 & 0 & 2 & 1 \\ -4 & 3 & 0 & -3 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -3 & 1 & 4 & -4 \\ 3 & -5 & 3 & -5 \\ 0 & 0 & 2 & 1 \\ -4 & 3 & 0 & -3 \end{array}\right] = -5 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -2 & 3 & -3 & 1 \\ 6 & 4 & 4 & 0 \\ 4 & -1 & 0 & 0 \\ -4 & -4 & -3 & 3 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -2 & 3 & -3 & 1 \\ 6 & 4 & 4 & 0 \\ 4 & -1 & 0 & 0 \\ -4 & -4 & -3 & 3 \end{array}\right] = 332 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -5 & 0 & 3 & -2 \\ -5 & -6 & -6 & 4 \\ 1 & -2 & 0 & 0 \\ -6 & 1 & 6 & -2 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -5 & 0 & 3 & -2 \\ -5 & -6 & -6 & 4 \\ 1 & -2 & 0 & 0 \\ -6 & 1 & 6 & -2 \end{array}\right] = 216 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -5 & -4 & -2 & -3 \\ -5 & -1 & 0 & 1 \\ 0 & -1 & -3 & 0 \\ 2 & 2 & -6 & -3 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -5 & -4 & -2 & -3 \\ -5 & -1 & 0 & 1 \\ 0 & -1 & -3 & 0 \\ 2 & 2 & -6 & -3 \end{array}\right] = -307 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} 6 & -6 & 1 & 0 \\ -4 & -2 & 2 & 0 \\ -6 & 4 & -1 & -1 \\ -3 & 4 & 1 & 0 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} 6 & -6 & 1 & 0 \\ -4 & -2 & 2 & 0 \\ -6 & 4 & -1 & -1 \\ -3 & 4 & 1 & 0 \end{array}\right] = -70 \]
Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -6 & -2 & -1 & 3 \\ -2 & 0 & 0 & -4 \\ 1 & 1 & 3 & -5 \\ -4 & 0 & 1 & 3 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -6 & -2 & -1 & 3 \\ -2 & 0 & 0 & -4 \\ 1 & 1 & 3 & -5 \\ -4 & 0 & 1 & 3 \end{array}\right] = -108 \]