1. Power Method for finding dominant eigenvalue ...
`[[2,3],[4,10]]`

Solution:

`A=`

2 3 4 10

`x_0=`

1 1

`1^(st)` Iteration

`A x_0 =`

2 3 4 10

1 1

`=`

5 14

and by scaling we obtain the approximation

`x_1=`

`1/14`

5 14

`=`

0.35714 1

`2^(nd)` Iteration

`A x_1 =`

2 3 4 10

0.35714 1

`=`

3.71429 11.42857

and by scaling we obtain the approximation

`x_2=`

`1/11.42857`

3.71429 11.42857

`=`

0.325 1

`3^(rd)` Iteration

`A x_2 =`

2 3 4 10

0.325 1

`=`

3.65 11.3

and by scaling we obtain the approximation

`x_3=`

`1/11.3`

3.65 11.3

`=`

0.32301 1

`4^(th)` Iteration

`A x_3 =`

2 3 4 10

0.32301 1

`=`

3.64602 11.29204

and by scaling we obtain the approximation

`x_4=`

`1/11.29204`

3.64602 11.29204

`=`

0.32288 1

`:.` The dominant eigenvalue `lamda=11.29204`

and the dominant eigenvector is :

`=`

0.32288 1

---