# Worksheet For Matrices

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

1) Find the addition of two matrices

A =

 1 3 7 4

B =

 -3 1 8 -7

2) Find the addition of two matrices

A =

 5 11 3 -2

B =

 7 9 8 7

3) Find the addition of two matrices

A =

 -1 2 3 5 8 -10

B =

 1 5 7 -3 2 0

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

5) Find the addition of two matrices

A =

 -3 4 -8 5 5 6

B =

 1 2 3 4 -5 3

 Practice question for subtraction Solution

1) Find the subtraction of two matrices

A =

 1 3 7 4

B =

 -3 1 8 -7

2) Find the subtraction of two matrices

A =

 5 11 3 -2

B =

 7 9 8 7

3) Find the addition of two matrices

A =

 -1 2 3 5 8 -10

B =

 1 5 7 -3 2 0

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

5) Find the addition of two matrices

A =

 -3 4 -8 5 5 6

B =

 1 2 3 4 -5 3

 Practice question for multiplication Solution

1) Find the multiplication of two matrices

A =

 1 3 7 4

B =

 -3 1 8 -7

2) Find the multiplication of two matrices

A =

 5 11 3 -2

B =

 7 9 8 7

3) Find the multiplication of two matrices

A =

 -1 3 0 5

B =

 1 2 -3 7

 Practice question of rank method Solution

 1) Find the following linear equations by using rank method of matrix2x + y + z = 5x + y + z = 4x - y + 2z = 1 Solution 2) Find the following linear equations by using rank method of matrixx + 2y + z = 72x - y + 2z = 4x + y - 2z = -1 Solution 3) Find the following linear equations by using rank method of matrix2x + 5y + 7z = 52x + y + z = 92x + y - z = 0 Solution 4) Find the following linear equations by using rank method of matrix3x + y - z = 22x - y + 2z = 62x + y - 2z = -2 Solution 5) Find the following linear equations by using rank method of matrix2x - y + 3z = 9x + y + z = 6x - 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

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 method2x + y + z = 5x + y + z = 4x - y + 2z = 1                                                         Solution 2) Solve the following homogeneous system of linear equations using inversion methodx + 2y + z = 72x - y + 2z = 4x + y - 2z = -1                                                        Solution 3) Solve the following homogeneous system of linear equations using inversion methodx + y + z = 4x - y + z = 22x + y - z = 1                                                          Solution 4) Solve the following homogeneous system of linear equations using inversion method2x + 5y + 7z = 52x + y + z = 92x + y - z = 0                                                          Solution 5) Solve the following homogeneous system of linear equations using inversion method3x + y - z = 22x - y + 2z = 62x + 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

Question 2 :

Determine the characteristic vector of the matrix

 1 1 3 1 5 1 3 1 1

Question 3 :

Determine the characteristic vector of the matrix

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

Question 4 :

Determine the characteristic vector of the matrix

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

Question 5 :

Determine the characteristic vector of the matrix

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

 Characteristic Roots of Matrix Solution

Question 1 :

Determine the characteristic roots of the matrix

 5 0 1 0 -2 0 1 0 5

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

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

Question 5 : worksheet for matrices

Determine the characteristic roots of the matrix

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

 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

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

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