M2- Invertable matrices


Example 1

M2- Invertable matrices (ver. 1)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 3 & -11 & -10 & 2 \\ -2 & 5 & 5 & 2 \\ 2 & -9 & -8 & 3 \\ -1 & -1 & 1 & 12 \end{array}\right]\]

Answer.

This matrix is invertible.


Example 2

M2- Invertable matrices (ver. 2)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 2 & -1 & 3 & -12 \\ 0 & 1 & 5 & -11 \\ -1 & 0 & -1 & 6 \\ 1 & -1 & 1 & -4 \end{array}\right]\]

Answer.

This matrix is invertible.


Example 3

M2- Invertable matrices (ver. 3)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 1 & -3 & 1 & -12 \\ -2 & -5 & 11 & -9 \\ -2 & -5 & 12 & -9 \\ 0 & 3 & -4 & 9 \end{array}\right]\]

Answer.

This matrix is not invertible.


Example 4

M2- Invertable matrices (ver. 4)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 1 & 2 & -2 & -10 \\ 0 & 1 & -3 & -11 \\ 0 & 1 & -2 & -7 \\ -1 & 0 & -4 & -11 \end{array}\right]\]

Answer.

This matrix is invertible.


Example 5

M2- Invertable matrices (ver. 5)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 1 & 2 & -5 & 9 \\ 0 & 1 & -2 & 4 \\ 0 & 0 & 1 & -2 \\ 1 & -1 & -1 & 1 \end{array}\right]\]

Answer.

This matrix is not invertible.


Example 6

M2- Invertable matrices (ver. 6)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 2 & 2 & 6 & 5 \\ 1 & 3 & 5 & 2 \\ 0 & -5 & -9 & -8 \\ 1 & 0 & 3 & 5 \end{array}\right]\]

Answer.

This matrix is invertible.


Example 7

M2- Invertable matrices (ver. 7)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 0 & 1 & 0 & 5 \\ 4 & -3 & 1 & -12 \\ 1 & -2 & 0 & -10 \\ -2 & 3 & -2 & 10 \end{array}\right]\]

Answer.

This matrix is invertible.


Example 8

M2- Invertable matrices (ver. 8)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 1 & -4 & -3 & 2 \\ -2 & 9 & 7 & -3 \\ -4 & 11 & 8 & -8 \\ 1 & -6 & -3 & 11 \end{array}\right]\]

Answer.

This matrix is invertible.


Example 9

M2- Invertable matrices (ver. 9)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} -2 & -7 & 0 & 12 \\ 1 & 3 & 0 & -5 \\ -2 & -4 & 1 & 3 \\ 1 & 2 & 3 & -11 \end{array}\right]\]

Answer.

This matrix is invertible.


Example 10

M2- Invertable matrices (ver. 10)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 1 & 1 & 2 & 6 \\ -1 & 2 & 4 & 11 \\ 0 & -3 & -5 & -10 \\ 0 & 1 & 2 & 6 \end{array}\right]\]

Answer.

This matrix is invertible.


Example 11

M2- Invertable matrices (ver. 11)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 1 & -3 & 1 & 7 \\ 0 & 1 & -1 & -2 \\ 1 & -3 & 2 & 6 \\ 0 & -5 & 3 & 12 \end{array}\right]\]

Answer.

This matrix is not invertible.


Example 12

M2- Invertable matrices (ver. 12)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 1 & 0 & -2 & -5 \\ 0 & 1 & 4 & 10 \\ 0 & 0 & 1 & 3 \\ -3 & -2 & 1 & 4 \end{array}\right]\]

Answer.

This matrix is not invertible.


Example 13

M2- Invertable matrices (ver. 13)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 1 & 1 & 3 & -7 \\ 0 & 1 & -2 & -5 \\ 0 & 0 & 0 & 1 \\ 0 & 2 & -4 & -10 \end{array}\right]\]

Answer.

This matrix is not invertible.


Example 14

M2- Invertable matrices (ver. 14)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 1 & -1 & -5 & -3 \\ 0 & 1 & 3 & 1 \\ 0 & 1 & 4 & 2 \\ 2 & -3 & -11 & -5 \end{array}\right]\]

Answer.

This matrix is not invertible.


Example 15

M2- Invertable matrices (ver. 15)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} -3 & -5 & 2 & 2 \\ -1 & -1 & 1 & 3 \\ 1 & 0 & -2 & -7 \\ 4 & 7 & -1 & 1 \end{array}\right]\]

Answer.

This matrix is invertible.


Example 16

M2- Invertable matrices (ver. 16)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} -2 & 1 & 7 & 0 \\ -2 & 1 & 6 & -1 \\ -3 & 1 & 12 & 3 \\ 1 & -1 & 0 & 5 \end{array}\right]\]

Answer.

This matrix is not invertible.


Example 17

M2- Invertable matrices (ver. 17)

Explain why the following matrix is or is not invertible.

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

Answer.

This matrix is not invertible.


Example 18

M2- Invertable matrices (ver. 18)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} -2 & 1 & -1 & -9 \\ -2 & -1 & -2 & -10 \\ 1 & 0 & 1 & 6 \\ 1 & 1 & 1 & 5 \end{array}\right]\]

Answer.

This matrix is invertible.


Example 19

M2- Invertable matrices (ver. 19)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} -3 & -8 & 9 & 3 \\ 3 & 1 & 12 & -8 \\ 2 & 0 & 10 & -5 \\ 2 & 4 & -2 & -3 \end{array}\right]\]

Answer.

This matrix is not invertible.


Example 20

M2- Invertable matrices (ver. 20)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 1 & 2 & 5 & -2 \\ -3 & -5 & -11 & 2 \\ 0 & -2 & -7 & 7 \\ 0 & 1 & 5 & -5 \end{array}\right]\]

Answer.

This matrix is not invertible.


Example 21

M2- Invertable matrices (ver. 21)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 1 & -1 & 2 & 0 \\ 5 & -4 & 10 & 1 \\ 4 & -4 & 9 & 0 \\ -2 & 6 & -7 & 4 \end{array}\right]\]

Answer.

This matrix is not invertible.


Example 22

M2- Invertable matrices (ver. 22)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 1 & -2 & -4 & -11 \\ 1 & -1 & -2 & -6 \\ 2 & -2 & -3 & -10 \\ -1 & 1 & 3 & 8 \end{array}\right]\]

Answer.

This matrix is not invertible.


Example 23

M2- Invertable matrices (ver. 23)

Explain why the following matrix is or is not invertible.

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

Answer.

This matrix is not invertible.


Example 24

M2- Invertable matrices (ver. 24)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 1 & -8 & -3 & 3 \\ 0 & 1 & 0 & 1 \\ 1 & -7 & -2 & 1 \\ 1 & 0 & -3 & 11 \end{array}\right]\]

Answer.

This matrix is not invertible.


Example 25

M2- Invertable matrices (ver. 25)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 2 & 1 & -10 & -7 \\ -2 & 1 & 3 & -2 \\ -1 & -1 & 7 & 6 \\ -2 & 2 & -4 & -10 \end{array}\right]\]

Answer.

This matrix is not invertible.


Example 26

M2- Invertable matrices (ver. 26)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 3 & -2 & 11 & -9 \\ 0 & 1 & 4 & 7 \\ 1 & -1 & 2 & -6 \\ 2 & -1 & 10 & -2 \end{array}\right]\]

Answer.

This matrix is invertible.


Example 27

M2- Invertable matrices (ver. 27)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 6 & -8 & -8 & -6 \\ -5 & 6 & 7 & 7 \\ 1 & -2 & 2 & 7 \\ -5 & 7 & 6 & 3 \end{array}\right]\]

Answer.

This matrix is not invertible.


Example 28

M2- Invertable matrices (ver. 28)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 1 & -5 & -2 & 10 \\ -1 & 6 & 3 & -11 \\ 1 & 0 & 4 & 7 \\ 0 & -5 & -6 & 3 \end{array}\right]\]

Answer.

This matrix is not invertible.


Example 29

M2- Invertable matrices (ver. 29)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 1 & 0 & 0 & -3 \\ -2 & -1 & 1 & 10 \\ -1 & 0 & 0 & 2 \\ 0 & 1 & -2 & -6 \end{array}\right]\]

Answer.

This matrix is invertible.


Example 30

M2- Invertable matrices (ver. 30)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 1 & 0 & 2 & -5 \\ 3 & 1 & 5 & -12 \\ 0 & 0 & 1 & -3 \\ -1 & 0 & -3 & 8 \end{array}\right]\]

Answer.

This matrix is not invertible.


Example 31

M2- Invertable matrices (ver. 31)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 0 & -5 & 4 & -5 \\ 1 & -4 & 4 & -4 \\ 1 & 0 & 1 & 0 \\ -1 & 10 & -10 & 10 \end{array}\right]\]

Answer.

This matrix is not invertible.


Example 32

M2- Invertable matrices (ver. 32)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 0 & 1 & 1 & 0 \\ -1 & 6 & 1 & 12 \\ -1 & 5 & 1 & 9 \\ -1 & 6 & 4 & 4 \end{array}\right]\]

Answer.

This matrix is invertible.


Example 33

M2- Invertable matrices (ver. 33)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 1 & -1 & 3 & 3 \\ 0 & 1 & 3 & -2 \\ -1 & 2 & 6 & -5 \\ 0 & 1 & 8 & -2 \end{array}\right]\]

Answer.

This matrix is not invertible.


Example 34

M2- Invertable matrices (ver. 34)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 1 & 0 & -1 & -6 \\ 0 & 1 & 3 & 11 \\ -2 & -1 & 0 & 5 \\ -3 & -1 & 1 & 12 \end{array}\right]\]

Answer.

This matrix is invertible.


Example 35

M2- Invertable matrices (ver. 35)

Explain why the following matrix is or is not invertible.

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

Answer.

This matrix is not invertible.


Example 36

M2- Invertable matrices (ver. 36)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 1 & 2 & -7 & 8 \\ 1 & 3 & -8 & 7 \\ 1 & 4 & -8 & 4 \\ 1 & 4 & -5 & -1 \end{array}\right]\]

Answer.

This matrix is invertible.


Example 37

M2- Invertable matrices (ver. 37)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} -2 & 1 & -6 & -7 \\ -1 & 1 & -5 & -2 \\ 2 & 1 & -4 & 12 \\ 3 & -1 & 6 & 12 \end{array}\right]\]

Answer.

This matrix is invertible.


Example 38

M2- Invertable matrices (ver. 38)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 1 & 0 & -5 & -9 \\ 0 & 1 & -5 & -11 \\ 0 & 1 & -4 & -9 \\ -1 & 0 & 2 & 3 \end{array}\right]\]

Answer.

This matrix is not invertible.


Example 39

M2- Invertable matrices (ver. 39)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 1 & 4 & -2 & 8 \\ -1 & -3 & 2 & -9 \\ 0 & 3 & 1 & -8 \\ -2 & -7 & 2 & -6 \end{array}\right]\]

Answer.

This matrix is invertible.


Example 40

M2- Invertable matrices (ver. 40)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 1 & 2 & -9 & 5 \\ 1 & 3 & -11 & 8 \\ 1 & 3 & -10 & 8 \\ 0 & 2 & -1 & 6 \end{array}\right]\]

Answer.

This matrix is not invertible.


Example 41

M2- Invertable matrices (ver. 41)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 4 & -3 & -7 & -2 \\ -1 & 1 & 3 & 0 \\ -4 & 0 & -7 & 8 \\ 2 & 1 & 9 & -6 \end{array}\right]\]

Answer.

This matrix is not invertible.


Example 42

M2- Invertable matrices (ver. 42)

Explain why the following matrix is or is not invertible.

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

Answer.

This matrix is not invertible.


Example 43

M2- Invertable matrices (ver. 43)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 1 & -1 & 1 & 1 \\ -3 & 4 & 1 & 8 \\ 5 & -5 & 6 & 7 \\ 5 & -5 & 1 & -3 \end{array}\right]\]

Answer.

This matrix is not invertible.


Example 44

M2- Invertable matrices (ver. 44)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 1 & 2 & -4 & 5 \\ -2 & -3 & 9 & -10 \\ 0 & 0 & 1 & -1 \\ -1 & -2 & 4 & -5 \end{array}\right]\]

Answer.

This matrix is not invertible.


Example 45

M2- Invertable matrices (ver. 45)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 2 & 0 & -4 & 5 \\ 3 & 1 & -3 & -1 \\ 1 & -1 & -4 & 9 \\ -1 & 0 & 2 & -2 \end{array}\right]\]

Answer.

This matrix is invertible.


Example 46

M2- Invertable matrices (ver. 46)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 1 & 2 & 4 & -2 \\ -1 & -3 & -8 & 2 \\ -1 & -3 & -7 & 2 \\ 0 & 2 & 8 & 0 \end{array}\right]\]

Answer.

This matrix is not invertible.


Example 47

M2- Invertable matrices (ver. 47)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 1 & -3 & 0 & 1 \\ 4 & -11 & -1 & 7 \\ 1 & -3 & 1 & -4 \\ 1 & -8 & 3 & -3 \end{array}\right]\]

Answer.

This matrix is invertible.


Example 48

M2- Invertable matrices (ver. 48)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 1 & -1 & -2 & -2 \\ -5 & 6 & 7 & 5 \\ 4 & -5 & -4 & -1 \\ 2 & -2 & -7 & -10 \end{array}\right]\]

Answer.

This matrix is not invertible.


Example 49

M2- Invertable matrices (ver. 49)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} 7 & 3 & 12 & 11 \\ -1 & 1 & -5 & -11 \\ -2 & -1 & -3 & -2 \\ 1 & 2 & 3 & 1 \end{array}\right]\]

Answer.

This matrix is not invertible.


Example 50

M2- Invertable matrices (ver. 50)

Explain why the following matrix is or is not invertible.

\[\left[\begin{array}{rrrr} -2 & 7 & -10 & 9 \\ -1 & 3 & -4 & 3 \\ -1 & 2 & -1 & -1 \\ 3 & -4 & 3 & 6 \end{array}\right]\]

Answer.

This matrix is invertible.