Cofactors and Minors in Matrices

The video tutorial explains how to find minors and cofactors of a 3x3 matrix. It begins by defining minors as the determinant of a matrix formed by eliminating a specific row and column. The tutorial then demonstrates how to calculate the minors by evaluating 2x2 determinants. After finding all the minors, the video explains how to calculate cofactors using the formula involving the power of negative one and the corresponding minor. The tutorial provides step-by-step examples for each minor and cofactor calculation, ensuring a comprehensive understanding of the process.

What is the definition of a minor in the context of matrices?

• The sum of all elements in a row

• The determinant of a matrix formed by eliminating a row and a column

• The product of the diagonal elements

• The inverse of a matrix

How do you find the minor M(1,1) of a 3x3 matrix?

• By eliminating the first row and second column

• By eliminating the third row and third column

• By eliminating the second row and second column

• By eliminating the first row and first column

What is the determinant of a 2x2 matrix with rows [4, 5] and [-6, 9]?

• 72

• 54

• 66

• 36

What is the formula for calculating a cofactor C(i,j)?

• The product of the minor and (-1)^(i+j)

• The square of the minor

• The difference between the minor and its index

• The sum of the minor and its index

What is the cofactor C(1,2) if the minor M(1,2) is -18?

• -36

• 18

• -18

• 36

Which power of -1 is used to calculate the cofactor C(2,3)?

• Fourth power

• Fifth power

• Second power

• Third power

What is the cofactor C(3,1) if the minor M(3,1) is 7?

• -14

• 14

• -7

• 7

How is the sign factor determined in the cofactor calculation?

• By the division of the row and column indices

• By the product of the row and column indices

• By the difference of the row and column indices

• By the sum of the row and column indices

What is the cofactor C(2,2) if the minor M(2,2) is 9?

• -18

• 18

• -9

• 9

What is the cofactor C(3,3) if the minor M(3,3) is 10?

• 10

• -10

• -20

• 20