Cofactors and Determinants in Matrices

This lesson explains how to find the cofactor of a 2x2 matrix, which is used in cofactor expansion to determine the determinant of a square matrix. The cofactor of an element is calculated as (-1)^(i+j) times the minor of the element, where the minor is the determinant of the matrix formed by eliminating the row and column of the element. The video provides two examples: finding the cofactor of A(2,1) and B(2,2), demonstrating the calculation process and emphasizing the distinction between vertical bars for determinants and absolute values.

What is the primary use of cofactors in matrix operations?

• To perform matrix multiplication

• To find the inverse of a matrix

• To solve linear equations

• To calculate the determinant of a square matrix

How is the cofactor of an element in a matrix calculated?

• By taking the absolute value of the element

• By multiplying the element by its minor

• By raising -1 to the power of the sum of its indices and multiplying by its minor

• By adding the row and column indices

In the first example, what is the element in row two, column one of the matrix?

• 5

• 3

• 1

• 7

What is the determinant of a 1x1 matrix with an element of 7?

• 0

• 7

• 1

• -7

What is the cofactor of the element in row two, column one in the first example?

• 1

• -1

• 7

• -7

In the second example, what is the element in row two, column two of the matrix?

• 3

• 0

• -1

• 2

What is the determinant of a 1x1 matrix with an element of -1?

• 2

• 0

• 1

• -1

What is the cofactor of the element in row two, column two in the second example?

• -1

• 2

• 0

• 1

What does the vertical bar notation represent in the context of this lesson?

• Matrix multiplication

• Absolute value

• Inverse of a matrix

• Determinant of a matrix

What is the result of multiplying 1 by -1 in the context of the second example?

• 1

• -1

• 0

• 2