Worksheet For Matrices





In this page worksheet for matrices we are going to see practice problems of addition,subtraction and multiplication of two matrices.

Addition of two matrices:

Two and more matrices can be added if and only if they are having same order. If the order those matrices are not same then we cannot add those matrices.


Practice question for addition

Solution


1) Find the addition of two matrices

A =
 
1 3
7 4
 
 
B =
 
-3 1
8 -7
 

                                                                      Solution

2) Find the addition of two matrices

A =
 
5 11
3 -2
 
 
B =
 
7 9
8 7
 

                                                                      Solution

3) Find the addition of two matrices

A =
 
-1 2 3
5 8 -10
 
 
B =
 
1 5 7
-3 2 0
 

                                                                      Solution

4) Find the addition of two matrices

A =
 
1 2 -1
5 6 3
8 9 -10
 
 
B =
 
-1 0 5
3 4 2
1 4 -3
 

                                                                      Solution

5) Find the addition of two matrices

A =
 
-3 4
-8 5
5 6
 
 
B =
 
1 2
3 4
-5 3
 

                                                                      Solution


Practice question for subtraction

Solution


1) Find the subtraction of two matrices

A =
 
1 3
7 4
 
 
B =
 
-3 1
8 -7
 

                                                                      Solution

2) Find the subtraction of two matrices

A =
 
5 11
3 -2
 
 
B =
 
7 9
8 7
 

                                                                      Solution

3) Find the addition of two matrices

A =
 
-1 2 3
5 8 -10
 
 
B =
 
1 5 7
-3 2 0
 

                                                                      Solution

4) Find the addition of two matrices

A =
 
1 2 -1
5 6 3
8 9 -10
 
 
B =
 
-1 0 5
3 4 2
1 4 -3
 

                                                                      Solution

5) Find the addition of two matrices

A =
 
-3 4
-8 5
5 6
 
 
B =
 
1 2
3 4
-5 3
 

                                                                      Solution


Practice question for multiplication

Solution


1) Find the multiplication of two matrices

A =
 
1 3
7 4
 
 
B =
 
-3 1
8 -7
 

                                                                      Solution

2) Find the multiplication of two matrices

A =
 
5 11
3 -2
 
 
B =
 
7 9
8 7
 

                                                                      Solution

3) Find the multiplication of two matrices

A =
 
-1 3
0 5
 
 
B =
 
1 2
-3 7
 

                                                                      Solution


Practice question of rank method

Solution


1) Find the following linear equations by using rank method of matrix

2x + y + z = 5

x + y + z = 4

x - y + 2z = 1

Solution

2) Find the following linear equations by using rank method of matrix

x + 2y + z = 7

2x - y + 2z = 4

x + y - 2z = -1

Solution

3) Find the following linear equations by using rank method of matrix

2x + 5y + 7z = 52

x + y + z = 9

2x + y - z = 0

Solution

4) Find the following linear equations by using rank method of matrix

3x + y - z = 2

2x - y + 2z = 6

2x + y - 2z = -2

Solution

5) Find the following linear equations by using rank method of matrix

2x - y + 3z = 9

x + y + z = 6

x - y + z = 2

Solution


Practice question of Minor of matrix

Solution


(1) Find the minor of the matrix

 
2 1 1
1 1 1
1 -1 2
 

Solution

(2) Find the minor of the matrix

 
1 2 3
1 1 1
2 3 4
 

Solution

(3) Find the minor of the matrix

 
6 2 3
3 1 1
10 3 4
 

Solution

(4) Find the minor of the matrix

 
1 1 -1
2 -3 4
3 -2 3
 

Solution

(5) Find the minor of the matrix

 
4 2 1
6 3 4
2 1 0
 

Solution


Practice question of Adjoint of matrix

Solution


1) Find the adjoint of the following matrix

 
2 1 1
1 1 1
1 -1 2
 

Solution

2) Find the adjoint of the following matrix

 
1 2 3
1 1 1
2 3 4
 

Solution

3) Find the adjoint of the following matrix

 
6 2 3
3 1 1
10 3 4
 

Solution

4) Find the adjoint of the following matrix

 
1 1 -1
2 -3 4
3 -2 3
 

Solution

5) Find the adjoint of the following matrix

 
4 2 1
6 3 4
2 1 0
 

Solution


Practice question of rank method

Solution


1) Find the rank of the following matrix

 
2 1 1 5
1 1 1 4
1 -1 2 1
 

Solution

2) Find the rank of the following matrix

 
1 2 1 7
2 -1 2 4
1 1 -2 -1
 

Solution

3) Find the rank of the following matrix

 
2 5 7 52
1 1 1 9
2 1 -1 0
 

Solution

4) Find the rank of the following matrix

 
3 1 -1 2
2 -1 2 6
2 1 -2 -2
 

Solution

5) Find the rank of the following matrix

 
2 -1 3 9
1 1 1 6
1 -1 1 2
 

Solution


Practice question of inverse of matrix

Solution


1) Find the inverse of the following matrix

 
2 1 1
1 1 1
1 -1 2
 

Solution

2) Find the inverse of the following matrix

 
1 2 1
2 -1 2
1 1 -2
 

Solution

3) Find the inverse of the following matrix

 
6 2 3
3 1 1
10 3 4
 

Solution

4) Find the inverse of the following matrix

 
2 5 7
1 1 1
2 1 -1
 

Solution

5) Find the inverse of the following matrix

 
3 1 -1
2 -1 2
2 1 -2
 

Solution


Practice question of solving by inversion method

Solution


1) Solve the following homogeneous system of linear equations using inversion method

2x + y + z = 5

x + y + z = 4

x - y + 2z = 1                                                         Solution

2) Solve the following homogeneous system of linear equations using inversion method

x + 2y + z = 7

2x - y + 2z = 4

x + y - 2z = -1                                                        Solution

3) Solve the following homogeneous system of linear equations using inversion method

x + y + z = 4

x - y + z = 2

2x + y - z = 1                                                          Solution

4) Solve the following homogeneous system of linear equations using inversion method

2x + 5y + 7z = 52

x + y + z = 9

2x + y - z = 0                                                          Solution

5) Solve the following homogeneous system of linear equations using inversion method

3x + y - z = 2

2x - y + 2z = 6

2x + y - 2z = -2                                                       Solution


Characteristic Vectors of Matrix

Solution


Question 1 :

Determine the characteristic vector of the matrix

 
5 0 1
0 -2 0
1 0 5
 



Solution

Question 2 :

Determine the characteristic vector of the matrix

 
1 1 3
1 5 1
3 1 1
 



Solution

Question 3 :

Determine the characteristic vector of the matrix

 
-2 2 -3
2 1 -6
-1 -2 0
 



Solution


Question 4 :

Determine the characteristic vector of the matrix

 
4 -20 -10
-2 10 4
6 -30 -13
 



Solution

Question 5 :

Determine the characteristic vector of the matrix

 
11 -4 -7
7 -2 -5
10 -4 -6
 



Solution


Characteristic Roots of Matrix

Solution


Question 1 :

Determine the characteristic roots of the matrix

 
5 0 1
0 -2 0
1 0 5
 



Solution

worksheet for matrices worksheet for matrices

worksheet for matrices worksheet for matrices

worksheet for matrices worksheet for matrices

worksheet for matrices worksheet for matr

worksheet for matrices worksheet for matrices

worksheet for matrices worksheet for matr

Question 2 :

Determine the characteristic roots of the matrix

 
1 1 3
1 5 1
3 1 1
 



Solution

Question 3 :

Determine the characteristic roots of the matrix

 
-2 2 -3
2 1 -6
-1 -2 0
 



Solution

Question 4 :   worksheet for matrices

Determine the characteristic roots of the matrix

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



Solution

Question 5 : worksheet for matrices

Determine the characteristic roots of the matrix

 
11 -4 -7
7 -2 -5
10 -4 -6
 



Solution


Diagonalization of Matrix

Solution


Question 1 :

Diagonalize the following matrix

 
5 0 1
0 -2 0
1 0 5
 




Solution

Question 2 :

Diagonalize the following matrix

 
1 1 3
1 5 1
3 1 1
 




Solution

Question 3 :

Diagonalize the following matrix

 
-2 2 -3
2 1 -6
-1 -2 0
 




Solution

Question 4 :

Diagonalize the following matrix

 
4 -20 -10
-2 10 4
6 -30 -13
 




Solution

Question 5 :

Diagonalize the following matrix

 
11 -4 -7
7 -2 -5
10 -4 -6
 




Solution






Worksheet for Matrices to Matrix Introduction