Understanding Minors and Cofactors in Matrices

The video tutorial explains how to find minors and cofactors of a 2x2 matrix. It begins with an introduction to the concepts of minors and cofactors, followed by a detailed calculation of minors by eliminating specific rows and columns. The tutorial clarifies the notation used for determinants to avoid confusion with absolute values. It then demonstrates how to calculate cofactors using the minors and the powers of negative one. The video concludes with an explanation of how the powers of negative one affect the sign of the cofactors.

What is the minor of an element in a matrix?

• The inverse of the matrix

• The sum of all elements in the matrix

• The determinant of the matrix formed by eliminating the row and column of the element

• The product of the element and its adjacent elements

How is the determinant of a 1x1 matrix determined?

• By using the element itself as the determinant

• By taking the absolute value of the element

• By multiplying the element by itself

• By adding the element to zero

How do you find minor 1,2 in a 2x2 matrix?

• By eliminating row 1 and column 2 and finding the determinant of the remaining matrix

• By multiplying the elements in row 1 and column 2

• By adding all elements in row 1 and column 2

• By finding the inverse of the matrix

Which of the following is true about the determinant of a 1x1 matrix?

• It is always zero

• It is always positive

• It is the square of the element

• It is the element itself

Why might vertical bars be confusing when representing determinants of 1x1 matrices?

• They are only used for larger matrices

• They are not commonly used in mathematics

• They can be mistaken for absolute value symbols

• They look similar to brackets

What is the formula for calculating a cofactor?

• The product of the row and column indices

• The minor divided by the sum of the row and column indices

• The sum of the row and column indices

• Negative one raised to the power of the sum of the row and column indices, times the minor

What is the result when the exponent of negative one is even?

• Negative one

• Undefined

• Zero

• Positive one

What happens to the sign of a cofactor if the sum of the row and column indices is odd?

• It becomes negative

• It becomes positive

• It becomes zero

• It remains unchanged

What is the cofactor of an element if its minor is 5 and the sum of its row and column indices is 4?

• 5

• -5

• 0

• 10

What is the cofactor of an element if its minor is -6 and the sum of its row and column indices is 3?

• -6

• 6

• 0

• -12