Characteristic roots Worksheet





In this page characteristic roots worksheet we are going to see some practice questions that how to find characteristic roots of the matrix.

Definition :

The eigen vector can be obtained from (A- λI)X = 0. Here A is the given matrix λ is a scalar,I is the unit matrix and X is the columns matrix formed by the variables a,b and c.

Another name of characteristic Vector:

Characteristic vector are also known as latent vectors or Eigen vectors of a matrix.


Characteristic roots  of matrix

Practice questions


(1) Determine the characteristic roots of the matrix

 
5 0 1
0 -2 0
1 0 5
 

Solution

(2) Determine the characteristic roots of the matrix

 
1 1 3
1 5 1
3 1 1
 

Solution

(3) Determine the characteristic roots of the matrix

 
-2 2 -3
2 1 -6
-1 -2 0
 

Solution

(4) Determine the characteristic roots of the matrix

 
4 -20 -10
-2 10 4
6 -30 -13
 

Solution

(5) Determine the characteristic roots of the matrix

 
11 -4 -7
7 -2 -5
10 -4 -6
 

characteristic roots worksheet  characteristic roots worksheet

Solution



“Mathematics, without this we can do nothing in our life. Each and everything around us is math.

Math is not only solving problems and finding solutions and it is also doing many things in our day to day life.  They are: 

It subtracts sadness and adds happiness in our life.    

It divides sorrow and multiplies forgiveness and love.

Some people would not be able accept that the subject Math is easy to understand. That is because; they are unable to realize how the life is complicated. The problems in the subject Math are easier to solve than the problems in our real life. When we people are able to solve all the problems in the complicated life, why can we not solve the simple math problems?

Many people think that the subject math is always complicated and it exists to make things from simple to complicate. But the real existence of the subject math is to make things from complicate to simple.”





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