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Determinant of a 3x3 Matrix

Total questions: 10

Worksheet time: 5mins

Name
Class
Date
1.

What is the formula to calculate the determinant of a 3x3 matrix?

a)

det(A) = a(ei + fh) - b(di - fg) + c(dh - eg)

b)

det(A) = a(ei − fh) − b(di − fg) + c(dh − eg)

c)

det(A) = a(ei - fh) + b(di + fg) - c(dh - eg)

d)

det(A) = a(ei - fh) - b(di - fg) - c(dh - eg)

2.

Calculate the determinant of the matrix: [[2, 3, 1], [4, 5, 2], [1, 0, 3]]

a)

2

b)

7

c)

10

d)

5

3.

What is the value of the determinant of a matrix if it is singular?

a)

0

b)

3

c)

1

d)

2

4.

Find the determinant of the matrix: [[-1, 2, 3], [0, 4, -2], [1, 3, 5]]

a)

-42

b)

7

c)

10

d)

-12

5.

What is the property of determinants when two rows of a matrix are identical?

a)

Determinant is negative

b)

Determinant is 1

c)

Determinant is 0

d)

Determinant is undefined

6.

Calculate the determinant of the matrix: [[3, 1, 2], [0, -2, 1], [4, 3, 5]]

a)

-57

b)

12

c)

7

d)

-45

7.

What is the significance of the determinant of a matrix in terms of its invertibility?

a)

The determinant being positive guarantees invertibility.

b)

The determinant being zero guarantees invertibility.

c)

The determinant of a matrix being non-zero indicates its invertibility.

d)

The determinant being negative guarantees invertibility.

8.

Find the determinant of the matrix: [[-2, 1, 3], [4, 0, -1], [2, 3, 5]]

a)

-5

b)

77

c)

0

d)

12

9.

How does the determinant of a matrix change when its rows are interchanged?

a)

The determinant of a matrix changes sign when its rows are interchanged.

b)

The determinant of a matrix doubles when its rows are interchanged.

c)

The determinant of a matrix becomes zero when its rows are interchanged.

d)

The determinant of a matrix remains the same when its rows are interchanged.

10.

Calculate the determinant of the matrix: [[1, 2, 3], [0, 1, 4], [2, 3, 5]]

a)

-20

b)

-25

c)

7

d)

10