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

B = 

2) Find the addition of two matrices
A = 


B = 

3) Find the addition of two matrices
A = 


B = 

4) Find the addition of two matrices
A = 


B = 

5) Find the addition of two matrices
A = 


B = 

Practice question for subtraction 
Solution 
1) Find the subtraction of two matrices

B = 

2) Find the subtraction of two matrices
A = 


B = 

3) Find the addition of two matrices
A = 


B = 

4) Find the addition of two matrices
A = 


B = 

5) Find the addition of two matrices
A = 


B = 

Practice question for multiplication 
Solution 
1) Find the multiplication of two matrices

B = 

2) Find the multiplication of two matrices
A = 


B = 

3) Find the multiplication of two matrices
A = 


B = 

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  
2) Find the following linear equations by using rank method of matrix x + 2y + z = 7 2x  y + 2z = 4 x + y  2z = 1  
3) Find the following linear equations by using rank method of matrix 2x + 5y + 7z = 52 x + y + z = 9 2x + y  z = 0  
4) Find the following linear equations by using rank method of matrix 3x + y  z = 2 2x  y + 2z = 6 2x + y  2z = 2  
5) Find the following linear equations by using rank method of matrix 2x  y + 3z = 9 x + y + z = 6 x  y + z = 2 
Practice question of Minor of matrix 
Solution 
(1) Find the minor of the matrix


(2) Find the minor of the matrix


(3) Find the minor of the matrix


(4) Find the minor of the matrix


(5) Find the minor of the matrix


Practice question of Adjoint of matrix 
Solution 
1) Find the adjoint of the following matrix


2) Find the adjoint of the following matrix


3) Find the adjoint of the following matrix


4) Find the adjoint of the following matrix


5) Find the adjoint of the following matrix


Practice question of rank method 
Solution 
1) Find the rank of the following matrix


2) Find the rank of the following matrix


3) Find the rank of the following matrix


4) Find the rank of the following matrix


5) Find the rank of the following matrix


Practice question of inverse of matrix 
Solution 
1) Find the inverse of the following matrix


2) Find the inverse of the following matrix


3) Find the inverse of the following matrix


4) Find the inverse of the following matrix


5) Find the inverse of the following matrix


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

 
Question 2 : Determine the characteristic vector of the matrix

 
Question 3 : Determine the characteristic vector of the matrix

 
Question 4 : Determine the characteristic vector of the matrix

 
Question 5 : Determine the characteristic vector of the matrix


Characteristic Roots of Matrix 
Solution 
Question 1 : Determine the characteristic roots of the matrix

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Question 2 : Determine the characteristic roots of the matrix

 
Question 3 : Determine the characteristic roots of the matrix

 
Question 4 : worksheet for matrices Determine the characteristic roots of the matrix

 
Question 5 : worksheet for matrices Determine the characteristic roots of the matrix


Diagonalization of Matrix 
Solution 
Question 1 : Diagonalize the following matrix

 
Question 2 : Diagonalize the following matrix

 
Question 3 : Diagonalize the following matrix

 
Question 4 : Diagonalize the following matrix

 
Question 5 : Diagonalize the following matrix

