Linear Algebra : The Determinant

Study concepts, example questions & explanations for Linear Algebra

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Example Questions

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Example Question #1 : The Determinant

Calculate the determinant of matrix A where

Possible Answers:

45

Not Possible 

0

10

-50

Correct answer:

Not Possible 

Explanation:

The matrix must be square to calculate its determinant, therefore, it is not possible to calculate the determinant for this matrix.  

Example Question #2 : The Determinant

Calculate the determinant of matrix A where,

 

Possible Answers:

-7

12

7

0

17

Correct answer:

7

Explanation:

To calculate the determinant of a 2x2 matrix, we can use the equation 

Example Question #3 : The Determinant

Calculate the determinant of matrix A where, 

Possible Answers:

-504

0

-315

504

54

Correct answer:

504

Explanation:

To calculate the determinant of a 2x2 matrix, we can use the equation 

Example Question #4 : The Determinant

Calculate the determinant of matrix A where, 

Possible Answers:

15

0

-15

16

17

Correct answer:

16

Explanation:

To calculate the determinant of a 2x2 matrix, we can use the equation 

Example Question #5 : The Determinant

Calculate the determinant of matrix A where,

Possible Answers:

26

-26

0

15

-24

Correct answer:

-26

Explanation:

Calculating the determinant of a 3x3 matrix is more difficult than a 2x2 matrix.  To calculate the determinant of a 3x3 matrix, we use the following 

Example Question #6 : The Determinant

Calculate the determinant of matrix A where,

Possible Answers:

-50

-49

49

0

50

Correct answer:

-50

Explanation:

Calculating the determinant of a 3x3 matrix is more difficult than a 2x2 matrix.  To calculate the determinant of a 3x3 matrix, we use the following 

Example Question #7 : The Determinant

Calculate the determinant of .

Possible Answers:

Correct answer:

Explanation:

By definition,

,

therefore,

.

Example Question #8 : The Determinant

Calculate the determinant of 

Possible Answers:

Correct answer:

Explanation:

For simplicity, we will find the determinant by expanding along the second row.  Consider the following:

Example Question #9 : The Determinant

Calculate the determinant of .

Possible Answers:

Correct answer:

Explanation:

By definition,

.

Example Question #10 : The Determinant

Calculate the determinant of matrix A. 

 

Possible Answers:

Not possible

Correct answer:

Explanation:

In order to find the determinant of a 2x2 matrix, compute  :

 

 

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