G3 - Eigenvalues


Example 1

G3 - Eigenvalues (ver. 1)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} -17 & 80 \\ -4 & 19 \end{array}\right]\]

Answer.

\(\{ 3 , -1 \}\)


Example 2

G3 - Eigenvalues (ver. 2)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} 6 & 8 \\ -4 & -6 \end{array}\right]\]

Answer.

\(\{ 2 , -2 \}\)


Example 3

G3 - Eigenvalues (ver. 3)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} -22 & 72 \\ -6 & 20 \end{array}\right]\]

Answer.

\(\{ -4 , 2 \}\)


Example 4

G3 - Eigenvalues (ver. 4)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} -18 & 60 \\ -5 & 17 \end{array}\right]\]

Answer.

\(\{ 2 , -3 \}\)


Example 5

G3 - Eigenvalues (ver. 5)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

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

Answer.

\(\{ -3 , -2 \}\)


Example 6

G3 - Eigenvalues (ver. 6)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} -14 & 36 \\ -6 & 16 \end{array}\right]\]

Answer.

\(\{ 4 , -2 \}\)


Example 7

G3 - Eigenvalues (ver. 7)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} 0 & 12 \\ -1 & 7 \end{array}\right]\]

Answer.

\(\{ 4 , 3 \}\)


Example 8

G3 - Eigenvalues (ver. 8)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} -11 & 60 \\ -3 & 16 \end{array}\right]\]

Answer.

\(\{ 4 , 1 \}\)


Example 9

G3 - Eigenvalues (ver. 9)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} -2 & 0 \\ -4 & 2 \end{array}\right]\]

Answer.

\(\{ 2 , -2 \}\)


Example 10

G3 - Eigenvalues (ver. 10)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} -13 & 60 \\ -3 & 14 \end{array}\right]\]

Answer.

\(\{ 2 , -1 \}\)


Example 11

G3 - Eigenvalues (ver. 11)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

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

Answer.

\(\{ -2 , -1 \}\)


Example 12

G3 - Eigenvalues (ver. 12)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

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

Answer.

\(\{ -3 , -4 \}\)


Example 13

G3 - Eigenvalues (ver. 13)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} -1 & 6 \\ -1 & -6 \end{array}\right]\]

Answer.

\(\{ -4 , -3 \}\)


Example 14

G3 - Eigenvalues (ver. 14)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

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

Answer.

\(\{ -1 , 1 \}\)


Example 15

G3 - Eigenvalues (ver. 15)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} -9 & 12 \\ -6 & 9 \end{array}\right]\]

Answer.

\(\{ 3 , -3 \}\)


Example 16

G3 - Eigenvalues (ver. 16)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} 0 & 12 \\ -1 & -7 \end{array}\right]\]

Answer.

\(\{ -3 , -4 \}\)


Example 17

G3 - Eigenvalues (ver. 17)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} -2 & 0 \\ -2 & -4 \end{array}\right]\]

Answer.

\(\{ -2 , -4 \}\)


Example 18

G3 - Eigenvalues (ver. 18)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} 5 & 12 \\ -1 & -2 \end{array}\right]\]

Answer.

\(\{ 2 , 1 \}\)


Example 19

G3 - Eigenvalues (ver. 19)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} 10 & 14 \\ -7 & -11 \end{array}\right]\]

Answer.

\(\{ -4 , 3 \}\)


Example 20

G3 - Eigenvalues (ver. 20)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} -24 & 84 \\ -7 & 25 \end{array}\right]\]

Answer.

\(\{ -3 , 4 \}\)


Example 21

G3 - Eigenvalues (ver. 21)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} -11 & 40 \\ -2 & 7 \end{array}\right]\]

Answer.

\(\{ -1 , -3 \}\)


Example 22

G3 - Eigenvalues (ver. 22)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} -6 & 20 \\ -1 & 3 \end{array}\right]\]

Answer.

\(\{ -2 , -1 \}\)


Example 23

G3 - Eigenvalues (ver. 23)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} -5 & 12 \\ -1 & 2 \end{array}\right]\]

Answer.

\(\{ -1 , -2 \}\)


Example 24

G3 - Eigenvalues (ver. 24)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} -7 & 12 \\ -1 & 0 \end{array}\right]\]

Answer.

\(\{ -4 , -3 \}\)


Example 25

G3 - Eigenvalues (ver. 25)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} 3 & 0 \\ -7 & -4 \end{array}\right]\]

Answer.

\(\{ -4 , 3 \}\)


Example 26

G3 - Eigenvalues (ver. 26)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} -3 & 0 \\ -6 & 3 \end{array}\right]\]

Answer.

\(\{ 3 , -3 \}\)


Example 27

G3 - Eigenvalues (ver. 27)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} 20 & 72 \\ -6 & -22 \end{array}\right]\]

Answer.

\(\{ -4 , 2 \}\)


Example 28

G3 - Eigenvalues (ver. 28)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} 14 & 36 \\ -6 & -16 \end{array}\right]\]

Answer.

\(\{ -4 , 2 \}\)


Example 29

G3 - Eigenvalues (ver. 29)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} -5 & 8 \\ -4 & 7 \end{array}\right]\]

Answer.

\(\{ 3 , -1 \}\)


Example 30

G3 - Eigenvalues (ver. 30)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} -6 & 6 \\ -1 & -1 \end{array}\right]\]

Answer.

\(\{ -4 , -3 \}\)


Example 31

G3 - Eigenvalues (ver. 31)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} -15 & 48 \\ -4 & 13 \end{array}\right]\]

Answer.

\(\{ -3 , 1 \}\)


Example 32

G3 - Eigenvalues (ver. 32)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

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

Answer.

\(\{ 3 , 4 \}\)


Example 33

G3 - Eigenvalues (ver. 33)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} 22 & 72 \\ -6 & -20 \end{array}\right]\]

Answer.

\(\{ -2 , 4 \}\)


Example 34

G3 - Eigenvalues (ver. 34)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} -20 & 72 \\ -6 & 22 \end{array}\right]\]

Answer.

\(\{ 4 , -2 \}\)


Example 35

G3 - Eigenvalues (ver. 35)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} -20 & 48 \\ -8 & 20 \end{array}\right]\]

Answer.

\(\{ -4 , 4 \}\)


Example 36

G3 - Eigenvalues (ver. 36)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

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

Answer.

\(\{ 2 , 1 \}\)


Example 37

G3 - Eigenvalues (ver. 37)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

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

Answer.

\(\{ 3 , 2 \}\)


Example 38

G3 - Eigenvalues (ver. 38)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} 5 & 24 \\ -2 & -9 \end{array}\right]\]

Answer.

\(\{ -1 , -3 \}\)


Example 39

G3 - Eigenvalues (ver. 39)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} 5 & 12 \\ -1 & -2 \end{array}\right]\]

Answer.

\(\{ 1 , 2 \}\)


Example 40

G3 - Eigenvalues (ver. 40)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

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

Answer.

\(\{ -2 , -1 \}\)


Example 41

G3 - Eigenvalues (ver. 41)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

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

Answer.

\(\{ -4 , 1 \}\)


Example 42

G3 - Eigenvalues (ver. 42)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} 3 & 0 \\ -7 & -4 \end{array}\right]\]

Answer.

\(\{ -4 , 3 \}\)


Example 43

G3 - Eigenvalues (ver. 43)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} -31 & 140 \\ -7 & 32 \end{array}\right]\]

Answer.

\(\{ -3 , 4 \}\)


Example 44

G3 - Eigenvalues (ver. 44)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} -10 & 36 \\ -3 & 11 \end{array}\right]\]

Answer.

\(\{ -1 , 2 \}\)


Example 45

G3 - Eigenvalues (ver. 45)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} 15 & 36 \\ -6 & -15 \end{array}\right]\]

Answer.

\(\{ 3 , -3 \}\)


Example 46

G3 - Eigenvalues (ver. 46)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} -12 & 40 \\ -2 & 6 \end{array}\right]\]

Answer.

\(\{ -4 , -2 \}\)


Example 47

G3 - Eigenvalues (ver. 47)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} 14 & 48 \\ -4 & -14 \end{array}\right]\]

Answer.

\(\{ 2 , -2 \}\)


Example 48

G3 - Eigenvalues (ver. 48)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} -17 & 42 \\ -7 & 18 \end{array}\right]\]

Answer.

\(\{ -3 , 4 \}\)


Example 49

G3 - Eigenvalues (ver. 49)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

\[\left[\begin{array}{rr} 1 & 6 \\ -1 & -4 \end{array}\right]\]

Answer.

\(\{ -1 , -2 \}\)


Example 50

G3 - Eigenvalues (ver. 50)

Explain how to find the eigenvalues of the following \(2\times 2\) matrix:

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

Answer.

\(\{ 1 , 3 \}\)