# Linear Algebra : The Determinant

## Example Questions

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### Example Question #1 : The Determinant

Calculate the determinant of matrix A where

Not Possible

-50

45

0

10

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,

7

0

12

-7

17

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,

504

54

0

-504

-315

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,

0

-15

17

16

15

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,

15

-24

26

0

-26

-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,

0

49

-50

-49

50

-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 .

Explanation:

By definition,

,

therefore,

.

### Example Question #8 : The Determinant

Calculate the determinant of

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 .

Explanation:

By definition,

.

### Example Question #10 : The Determinant

Calculate the determinant of matrix A.

Not possible