## Matrix Determinant

In this page matrix determinant we are going to see how to find determinant for any matrix and examples based on this topic.

Definition :

For every square matrix A of order n with entries as real or complex numbers,we can associate a number called determinant of matrix A and it is denoted by |A| or det (A) or ∆.

Example 1:

Find determinant of the following matrix.

 3 4 1 0 -1 2 5 -2 6

Solution :

A=

 3 4 1 0 -1 2 5 -2 6

= 3

 -1 2 -2 6

-4

 0 2 5 6

+1

 0 -1 5 -2

=  3 [ -6-(-4) ] -4 [ 0-10 ]+1 [0-(-5)]

=  3 [ -6+4 ] -4 [ -10 ]+1 [5]

=  3 [ -2 ] -4 [ -10 ]+ 1 [5]

=  -6 + 40 + 5

=  -6 + 45

=  39

Example 2:

Find determinant of the following matrix.

 1 1 -1 2 1 -2 1 -1 1

Solution :

= 1

 1 -2 -1 1

-1

 2 -2 1 1

-1

 2 1 1 -1

=  1 [1-2 ] -1 [ 2-(-2) ] - 1 [-2-1]

=  1 [-1] -1 [ 2+2 ] - 1 [-3]

=  -1 -1 (4) + 3

=  -1 -4 + 3

=  -5 + 3

=  -2

Example 3:

Find determinant of the following matrix.

 1 2 3 -1 3 4 2 0 -1

Solution :

=1

 3 4 0 -1

-2

 -1 4 2 -1

+3

 -1 3 2 0

=  1 [ -3 - 0 ] -2 [ 1 - 8 ] + 3 [0 - 6]

=  1 [ -3 ] -2 [ -7 ] + 3 [- 6]

=   -3 + 14 - 18

=   -21 + 14

=   -7               matrix determinant   matrix determinant  matrix determinant

Quote on Mathematics

“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 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.”

2. Matrix Inverse Calculator - 2x2 Matrix

3. Matrix Inverse Calculator - 3x3 Matrix

4. Matrix Inverse Calculator - 4x4 Matrix

5. Cramer's Rule Calculator - 3x3 Matrix

6. Matrix Addition Calculator - 3x3 Matrix

7. Matrix Subtraction Calculator - 3x3 Matrix

8. Matrix Multiplication Calculator - 2x2 Matrix

9. Matrix Multiplication Calculator - 3x3 Matrix

10. Matrix Determinant Calculator - 3x3 & 2x2 Matrix

11. Matrix Addition Calculator - 2x2 Matrix

12. Matrix Subtraction Calculator- 2x2 Matrix

13. Matrix Addition Calculator - 4x4 Matrix

14. Matrix Subtraction Calculator- 4x4 Matrix

15. Matrix Multiplication Calculator - 4x4 Matrix

16. Matrix Determinant Calculator - 4x4 matrix

17. Squared Matrix Calculator

18. Transpose Matrix Calculator
The text passage provides a definition of matrix determinants and includes three examples of finding the determinant of 3x3 matrices, each with a detailed solution.
multiple_questions_with_answers
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
## Matrix Determinant

In this page matrix determinant we are going to see how to find determinant for any matrix and examples based on this topic.

Definition :

For every square matrix A of order n with entries as real or complex numbers,we can associate a number called determinant of matrix A and it is denoted by |A| or det (A) or ∆.

Example 1:

Find determinant of the following matrix.

 3 4 1 0 -1 2 5 -2 6

Solution :

A=

 3 4 1 0 -1 2 5 -2 6

= 3

 -1 2 -2 6

-4

 0 2 5 6

+1

 0 -1 5 -2

=  3 [ -6-(-4) ] -4 [ 0-10 ]+1 [0-(-5)]

=  3 [ -6+4 ] -4 [ -10 ]+1 [5]

=  3 [ -2 ] -4 [ -10 ]+ 1 [5]

=  -6 + 40 + 5

=  -6 + 45

=  39

Example 2:

Find determinant of the following matrix.

 1 1 -1 2 1 -2 1 -1 1

Solution :

= 1

 1 -2 -1 1

-1

 2 -2 1 1

-1

 2 1 1 -1

=  1 [1-2 ] -1 [ 2-(-2) ] - 1 [-2-1]

=  1 [-1] -1 [ 2+2 ] - 1 [-3]

=  -1 -1 (4) + 3

=  -1 -4 + 3

=  -5 + 3

=  -2

Example 3:

Find determinant of the following matrix.

 1 2 3 -1 3 4 2 0 -1

Solution :

=1

 3 4 0 -1

-2

 -1 4 2 -1

+3

 -1 3 2 0

=  1 [ -3 - 0 ] -2 [ 1 - 8 ] + 3 [0 - 6]

=  1 [ -3 ] -2 [ -7 ] + 3 [- 6]

=   -3 + 14 - 18

=   -21 + 14

=   -7               matrix determinant   matrix determinant  matrix determinant

Quote on Mathematics

“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 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.”

2. Matrix Inverse Calculator - 2x2 Matrix

3. Matrix Inverse Calculator - 3x3 Matrix

4. Matrix Inverse Calculator - 4x4 Matrix

5. Cramer's Rule Calculator - 3x3 Matrix

6. Matrix Addition Calculator - 3x3 Matrix

7. Matrix Subtraction Calculator - 3x3 Matrix

8. Matrix Multiplication Calculator - 2x2 Matrix

9. Matrix Multiplication Calculator - 3x3 Matrix

10. Matrix Determinant Calculator - 3x3 & 2x2 Matrix

11. Matrix Addition Calculator - 2x2 Matrix

12. Matrix Subtraction Calculator- 2x2 Matrix

13. Matrix Addition Calculator - 4x4 Matrix

14. Matrix Subtraction Calculator- 4x4 Matrix

15. Matrix Multiplication Calculator - 4x4 Matrix

16. Matrix Determinant Calculator - 4x4 matrix

17. Squared Matrix Calculator

18. Transpose Matrix Calculator
user
The text passage provides a definition of matrix determinants and includes three examples of finding the determinant of 3x3 matrices, each with a detailed solution.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS