G2 - Computing matrix determinants


Example 1

G2 - Computing matrix determinants (ver. 1)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} 4 & -2 & 0 & -2 \\ -3 & -2 & -3 & 4 \\ -5 & -2 & 1 & 4 \\ 5 & -5 & 0 & -5 \end{array}\right]\]

Answer.

\(240\)


Example 2

G2 - Computing matrix determinants (ver. 2)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} 4 & 0 & -5 & 6 \\ -5 & -2 & 2 & -6 \\ -5 & 1 & 4 & -6 \\ 4 & 0 & -5 & -6 \end{array}\right]\]

Answer.

\(-420\)


Example 3

G2 - Computing matrix determinants (ver. 3)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -6 & 4 & 5 & 2 \\ 6 & 4 & -5 & 3 \\ -3 & 4 & 3 & 2 \\ 0 & 0 & 1 & -3 \end{array}\right]\]

Answer.

\(60\)


Example 4

G2 - Computing matrix determinants (ver. 4)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} 3 & -4 & 2 & 3 \\ -4 & 6 & 5 & -2 \\ -2 & 0 & 1 & 0 \\ -5 & 4 & -6 & -4 \end{array}\right]\]

Answer.

\(34\)


Example 5

G2 - Computing matrix determinants (ver. 5)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -4 & -3 & 3 & -3 \\ -6 & 2 & -4 & -6 \\ 0 & 1 & -3 & 0 \\ -2 & -5 & 6 & 6 \end{array}\right]\]

Answer.

\(294\)


Example 6

G2 - Computing matrix determinants (ver. 6)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} 6 & 0 & 4 & 6 \\ -5 & 1 & 4 & 5 \\ 6 & 0 & 5 & -2 \\ 6 & 3 & -6 & 5 \end{array}\right]\]

Answer.

\(-1722\)


Example 7

G2 - Computing matrix determinants (ver. 7)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} 5 & 6 & 4 & 4 \\ 3 & -3 & 4 & 4 \\ -5 & -6 & 5 & -2 \\ 1 & 0 & 0 & -3 \end{array}\right]\]

Answer.

\(1143\)


Example 8

G2 - Computing matrix determinants (ver. 8)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} 6 & 2 & 6 & 5 \\ 0 & 1 & 0 & -3 \\ -4 & 2 & 6 & -2 \\ -3 & -2 & 2 & 4 \end{array}\right]\]

Answer.

\(-130\)


Example 9

G2 - Computing matrix determinants (ver. 9)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} 3 & 3 & -4 & 6 \\ 5 & 4 & 3 & 6 \\ 0 & 0 & 2 & 1 \\ -5 & -5 & 5 & 3 \end{array}\right]\]

Answer.

\(-83\)


Example 10

G2 - Computing matrix determinants (ver. 10)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} 4 & -2 & 2 & -4 \\ 0 & 3 & 0 & 1 \\ 6 & 5 & 5 & -5 \\ -3 & 5 & -2 & 4 \end{array}\right]\]

Answer.

\(-14\)


Example 11

G2 - Computing matrix determinants (ver. 11)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -4 & 0 & -2 & -4 \\ -2 & 0 & -4 & -3 \\ 6 & 3 & -2 & 5 \\ -6 & 1 & -5 & 4 \end{array}\right]\]

Answer.

\(-376\)


Example 12

G2 - Computing matrix determinants (ver. 12)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -4 & -6 & -6 & -6 \\ 6 & 6 & -5 & -6 \\ -3 & 1 & 0 & 0 \\ -6 & 2 & 2 & 3 \end{array}\right]\]

Answer.

\(-210\)


Example 13

G2 - Computing matrix determinants (ver. 13)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -6 & -5 & -3 & -4 \\ 4 & -5 & -6 & 2 \\ -5 & -5 & -4 & 2 \\ -3 & 1 & 0 & 0 \end{array}\right]\]

Answer.

\(442\)


Example 14

G2 - Computing matrix determinants (ver. 14)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -2 & 3 & -4 & -5 \\ 0 & 2 & 1 & 0 \\ 6 & 6 & 3 & -3 \\ -6 & -6 & -6 & 2 \end{array}\right]\]

Answer.

\(150\)


Example 15

G2 - Computing matrix determinants (ver. 15)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} 5 & -5 & 0 & 3 \\ 3 & -5 & 1 & -4 \\ 4 & 6 & -3 & 3 \\ 6 & -2 & 0 & -4 \end{array}\right]\]

Answer.

\(-184\)


Example 16

G2 - Computing matrix determinants (ver. 16)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -4 & -5 & -6 & -2 \\ 3 & -6 & 5 & -5 \\ 0 & 0 & 2 & 1 \\ 2 & 6 & -5 & -3 \end{array}\right]\]

Answer.

\(-189\)


Example 17

G2 - Computing matrix determinants (ver. 17)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -4 & -6 & -5 & 3 \\ -3 & 6 & -3 & 0 \\ -6 & 5 & -2 & 0 \\ 3 & -6 & -2 & 1 \end{array}\right]\]

Answer.

\(126\)


Example 18

G2 - Computing matrix determinants (ver. 18)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} 3 & 3 & 4 & 2 \\ -6 & -5 & -4 & -6 \\ -2 & 0 & 0 & 1 \\ -4 & -3 & -4 & 2 \end{array}\right]\]

Answer.

\(-56\)


Example 19

G2 - Computing matrix determinants (ver. 19)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -6 & 4 & -3 & 3 \\ -4 & 6 & 2 & 5 \\ 6 & -3 & -6 & 5 \\ 1 & 0 & 3 & 0 \end{array}\right]\]

Answer.

\(221\)


Example 20

G2 - Computing matrix determinants (ver. 20)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -5 & 5 & 2 & -6 \\ 6 & 6 & 2 & -4 \\ -3 & -6 & -3 & -5 \\ 0 & 1 & -3 & 0 \end{array}\right]\]

Answer.

\(2030\)


Example 21

G2 - Computing matrix determinants (ver. 21)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -2 & -5 & 3 & 4 \\ -4 & -6 & 6 & -2 \\ 3 & 1 & 0 & 0 \\ 3 & -3 & 5 & -4 \end{array}\right]\]

Answer.

\(94\)


Example 22

G2 - Computing matrix determinants (ver. 22)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -4 & -2 & 6 & 0 \\ 6 & -3 & 3 & -2 \\ -5 & -3 & -6 & 1 \\ 2 & 5 & 2 & 0 \end{array}\right]\]

Answer.

\(100\)


Example 23

G2 - Computing matrix determinants (ver. 23)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -2 & -3 & 2 & 2 \\ 6 & -3 & -6 & 3 \\ 1 & 2 & 0 & 0 \\ -2 & 2 & 6 & -3 \end{array}\right]\]

Answer.

\(-162\)


Example 24

G2 - Computing matrix determinants (ver. 24)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -6 & 3 & 3 & -4 \\ -6 & 0 & 5 & 2 \\ -6 & 0 & -6 & 3 \\ -4 & 1 & 3 & 3 \end{array}\right]\]

Answer.

\(-732\)


Example 25

G2 - Computing matrix determinants (ver. 25)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -5 & 5 & -6 & 0 \\ -4 & -4 & 3 & -3 \\ 3 & -2 & -3 & 0 \\ -2 & 2 & -6 & 1 \end{array}\right]\]

Answer.

\(-279\)


Example 26

G2 - Computing matrix determinants (ver. 26)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} 5 & -5 & 6 & 6 \\ -4 & -2 & 2 & 4 \\ -2 & 1 & 0 & 0 \\ -5 & 5 & 2 & -6 \end{array}\right]\]

Answer.

\(224\)


Example 27

G2 - Computing matrix determinants (ver. 27)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -6 & 0 & -5 & -3 \\ 4 & 0 & 5 & 2 \\ 2 & 2 & 6 & 5 \\ -2 & 1 & 2 & 4 \end{array}\right]\]

Answer.

\(60\)


Example 28

G2 - Computing matrix determinants (ver. 28)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -6 & 0 & -5 & 4 \\ -2 & 0 & -4 & 3 \\ -6 & 2 & -5 & 4 \\ -6 & 1 & -4 & 2 \end{array}\right]\]

Answer.

\(36\)


Example 29

G2 - Computing matrix determinants (ver. 29)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} 4 & -2 & 4 & -5 \\ -5 & 6 & -5 & 2 \\ 3 & 2 & 3 & -4 \\ 1 & 0 & 0 & -2 \end{array}\right]\]

Answer.

\(56\)


Example 30

G2 - Computing matrix determinants (ver. 30)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -5 & -5 & 2 & 2 \\ 2 & -4 & 3 & 6 \\ 1 & 0 & 0 & 2 \\ -2 & -3 & -5 & -3 \end{array}\right]\]

Answer.

\(279\)


Example 31

G2 - Computing matrix determinants (ver. 31)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -5 & 2 & 4 & -3 \\ 1 & 0 & -2 & 0 \\ -2 & -5 & -3 & -5 \\ -6 & 2 & -4 & 3 \end{array}\right]\]

Answer.

\(514\)


Example 32

G2 - Computing matrix determinants (ver. 32)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} 4 & 6 & 3 & 5 \\ -4 & 4 & 0 & -6 \\ -4 & -4 & 1 & 3 \\ 3 & -2 & 0 & -6 \end{array}\right]\]

Answer.

\(-1316\)


Example 33

G2 - Computing matrix determinants (ver. 33)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -4 & 5 & -5 & 0 \\ 2 & -4 & 5 & 3 \\ 3 & 4 & 5 & 1 \\ 6 & -6 & -2 & 0 \end{array}\right]\]

Answer.

\(948\)


Example 34

G2 - Computing matrix determinants (ver. 34)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} 6 & -3 & 6 & -6 \\ 3 & -4 & -2 & -3 \\ -3 & -3 & -2 & 4 \\ -2 & 0 & 1 & 0 \end{array}\right]\]

Answer.

\(375\)


Example 35

G2 - Computing matrix determinants (ver. 35)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -6 & 6 & 6 & 4 \\ 6 & -3 & 3 & -6 \\ 0 & -3 & 0 & 1 \\ 6 & 5 & -4 & 6 \end{array}\right]\]

Answer.

\(-2250\)


Example 36

G2 - Computing matrix determinants (ver. 36)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} 3 & 3 & -2 & 0 \\ -5 & 5 & 4 & 0 \\ 6 & 6 & -2 & 1 \\ -3 & 6 & -6 & 3 \end{array}\right]\]

Answer.

\(438\)


Example 37

G2 - Computing matrix determinants (ver. 37)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} 5 & 3 & -4 & -5 \\ 0 & 0 & 1 & 3 \\ 5 & 5 & 6 & -4 \\ 3 & -6 & -6 & 5 \end{array}\right]\]

Answer.

\(943\)


Example 38

G2 - Computing matrix determinants (ver. 38)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -2 & -5 & -6 & -2 \\ 0 & 1 & -3 & 0 \\ 2 & -4 & -2 & 6 \\ -5 & -2 & 4 & 6 \end{array}\right]\]

Answer.

\(1174\)


Example 39

G2 - Computing matrix determinants (ver. 39)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} 3 & 3 & -3 & 0 \\ -4 & 6 & -2 & 1 \\ -2 & -2 & 6 & -2 \\ 2 & -6 & 3 & 0 \end{array}\right]\]

Answer.

\(108\)


Example 40

G2 - Computing matrix determinants (ver. 40)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -3 & -2 & 5 & -3 \\ 5 & 0 & -5 & 6 \\ -2 & 0 & 4 & 2 \\ 3 & 1 & -4 & -4 \end{array}\right]\]

Answer.

\(-146\)


Example 41

G2 - Computing matrix determinants (ver. 41)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -6 & 3 & -6 & 6 \\ 0 & 0 & 3 & 1 \\ 6 & -2 & 3 & 5 \\ 4 & 2 & -5 & -4 \end{array}\right]\]

Answer.

\(-810\)


Example 42

G2 - Computing matrix determinants (ver. 42)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -6 & 5 & -3 & -2 \\ 3 & 0 & 1 & 0 \\ -3 & -6 & 4 & -4 \\ 6 & -4 & -2 & -3 \end{array}\right]\]

Answer.

\(723\)


Example 43

G2 - Computing matrix determinants (ver. 43)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -5 & -5 & 6 & 6 \\ 1 & 2 & 0 & 0 \\ 4 & 2 & -3 & -4 \\ -4 & -6 & 2 & 5 \end{array}\right]\]

Answer.

\(-61\)


Example 44

G2 - Computing matrix determinants (ver. 44)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -2 & -2 & 3 & 2 \\ -5 & 2 & -2 & 5 \\ 3 & 6 & 5 & -3 \\ 1 & 0 & -2 & 0 \end{array}\right]\]

Answer.

\(-190\)


Example 45

G2 - Computing matrix determinants (ver. 45)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} 4 & -5 & -3 & -5 \\ 0 & -3 & 0 & 1 \\ 2 & -6 & -5 & 6 \\ -5 & 5 & -6 & 3 \end{array}\right]\]

Answer.

\(-1012\)


Example 46

G2 - Computing matrix determinants (ver. 46)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -5 & -3 & 2 & -6 \\ -6 & 5 & -6 & 5 \\ -6 & -6 & 5 & 3 \\ 0 & 3 & 1 & 0 \end{array}\right]\]

Answer.

\(2346\)


Example 47

G2 - Computing matrix determinants (ver. 47)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} 3 & -3 & -3 & -6 \\ -3 & 4 & -2 & -6 \\ -3 & 1 & 0 & 0 \\ 4 & 4 & -5 & -5 \end{array}\right]\]

Answer.

\(-351\)


Example 48

G2 - Computing matrix determinants (ver. 48)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -4 & 6 & 5 & -3 \\ -4 & 6 & -6 & 1 \\ -4 & -6 & 6 & 0 \\ 6 & 4 & 3 & 0 \end{array}\right]\]

Answer.

\(1564\)


Example 49

G2 - Computing matrix determinants (ver. 49)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} -3 & -4 & -6 & 0 \\ 4 & -2 & -2 & -3 \\ 2 & 4 & -5 & 0 \\ 2 & -6 & 2 & 1 \end{array}\right]\]

Answer.

\(-964\)


Example 50

G2 - Computing matrix determinants (ver. 50)

Show how to compute the determinant of the following matrix.

\[\left[\begin{array}{rrrr} 2 & 5 & -3 & -5 \\ 3 & 4 & 4 & -5 \\ 3 & 0 & 0 & 1 \\ -6 & 6 & -5 & 4 \end{array}\right]\]

Answer.

\(1198\)