Diagonalization matrix worksheet

In this page diagonalization matrix worksheet we are going to see some practice question of the topic diagonalization matrix.

Definition :

A square matrix of order n is diagonalizable if it is having linearly independent eigen values.

We can say that the given matrix is diagonalizable if it is alike to the diagonal matrix. Then there exists a non singular matrix P such that P⁻¹ AP = D where D is a diagonal matrix.

Diagonalization of matrix

Practice question

(1) Diagonalize the following matrix

5 0 1
0 -2 0
1 0 5


(2) Diagonalize the following matrix

1 1 3
1 5 1
3 1 1


(3) Diagonalize the following matrix

-2 2 -3
2 1 -6
-1 -2 0


(4) Diagonalize the following matrix

4 -20 -10
-2 10 4
6 -30 -13

diagonalization matrix worksheet


(5) Diagonalize the following matrix

11 -4 -7
7 -2 -5
10 -4 -6


“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.”