Determinants and Matrix Properties

The video tutorial explains how to evaluate determinants of a 4x4 matrix A with a determinant of 7. It covers the properties of determinants, including calculating the determinant of 2A, A squared, A inverse, and A transpose. The tutorial uses determinant properties to simplify these calculations, providing a clear understanding of each step.

What is the determinant of matrix A?

• 16

• 7

• 49

• 4

If a matrix is multiplied by a constant, how is the determinant affected?

• It remains the same.

• It is multiplied by the constant.

• It is raised to the power of the constant.

• It is multiplied by the constant raised to the power of n.

What is the determinant of 2A if the determinant of A is 7?

• 14

• 28

• 112

• 49

Which property of determinants is used to find the determinant of 2A?

• Determinant of a transpose

• Determinant of a constant times a matrix

• Determinant of a product

• Determinant of a sum

How can A squared be expressed in terms of matrix multiplication?

• A + A

• A - A

• A * A

• A / A

What is the determinant of A squared if the determinant of A is 7?

• 49

• 14

• 28

• 112

What is the determinant of A inverse if the determinant of A is 7?

• 1/7

• 7

• 1

• 49

How is the determinant of A inverse related to the determinant of A?

• It is the same as the determinant of A.

• It is the square of the determinant of A.

• It is the reciprocal of the determinant of A.

• It is zero.

What is the determinant of A transpose if the determinant of A is 7?

• 7

• 14

• 49

• 1

How does the determinant of a transpose compare to the original matrix?

• It is always zero.

• It is the same as the original matrix.

• It is the reciprocal of the original matrix.

• It is double the original matrix.