Determinants and Cofactor Expansion

The video tutorial explains how to compute the determinant of a 3x3 matrix using cofactor expansion on the second row. It details the process of identifying cofactors and minors, simplifying the determinant calculation, and evaluating the final determinant value. The tutorial provides a step-by-step guide to understanding the method of cofactors, also known as expansion by minors, and concludes with the determinant value of the matrix.

What is the method used to compute the determinant of a 3x3 matrix in this tutorial?

• Gaussian Elimination

• Matrix Inversion

• Row Reduction

• Cofactor Expansion

In cofactor expansion, what is the term used for the determinant of the smaller matrix formed by eliminating a row and column?

• Adjugate

• Minor

• Inverse

• Transpose

For the element -3 in row two, what is the power to which -1 is raised in the cofactor calculation?

• 4

• 3

• 5

• 2

What are the elements of the 2x2 minor matrix used for the element -8 in row two?

• 15, 10, -5, -3

• 5, 10, -2, -3

• 5, 15, -2, -5

• 10, 15, -3, -5

What is the sign of the cofactor for the element -8 in row two?

• Undefined

• Zero

• Negative

• Positive

For the element -6 in row two, what is the power to which -1 is raised in the cofactor calculation?

• 5

• 4

• 3

• 2

What are the elements of the 2x2 minor matrix used for the element -6 in row two?

• 15, 10, -5, -3

• 5, 10, -2, -3

• 10, 15, -3, -5

• 5, 15, -2, -5

What is the final value of the determinant of matrix A?

• 0

• 5

• 15

• 10

Which operation is performed to evaluate each 2x2 determinant?

• Subtraction

• Division

• Addition

• Multiplication

What is the result of the expression 15 - 40 + 30 in the final evaluation?

• 15

• 0

• 5

• 10