### All Linear Algebra Resources

## Example Questions

### Example Question #1 : The Determinant

Calculate the determinant of matrix A where

**Possible Answers:**

Not Possible

-50

45

0

10

**Correct answer:**

Not Possible

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

0

12

-7

17

**Correct answer:**

7

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

54

0

-504

-315

**Correct answer:**

504

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:**

0

-15

17

16

15

**Correct answer:**

16

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:**

15

-24

26

0

-26

**Correct answer:**

-26

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:**

0

49

-50

-49

50

**Correct answer:**

-50

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:**

By definition,

,

therefore,

.

### Example Question #8 : The Determinant

Calculate the determinant of

**Possible Answers:**

**Correct answer:**

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:**

By definition,

.

### Example Question #10 : The Determinant

Calculate the determinant of matrix A.

**Possible Answers:**

Not possible

**Correct answer:**

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

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