Cofactors and Determinants of Matrices

The video tutorial by Mairi from V Teach Academy covers the calculation of determinants for 3x3 matrices. It begins with a review of 2x2 matrices and their determinant calculation. The tutorial introduces the concepts of minors and cofactors, explaining how to find them for elements in a matrix. The process of calculating the determinant of a 3x3 matrix is demonstrated step-by-step, using the sum of products of elements and their corresponding cofactors. The tutorial concludes with a summary of the process and a final determinant value for the example matrix.

What is the determinant of a 2x2 matrix in the form of [[a, b], [c, d]]?

• a + d - b - c

• ad - bc

• ab + cd

• a - b + c - d

What is the order of the matrix discussed for finding determinants in this section?

• 5x5

• 4x4

• 3x3

• 2x2

What is a minor of an element in a 3x3 matrix?

• The product of the element with its adjacent elements

• The determinant of the 2x2 matrix obtained by deleting the row and column of the element

• The sum of all elements in the matrix

• The average of all elements in the matrix

How do you find the minor of the element 3 in the given example?

• By subtracting the row and column sums from 3

• By adding all elements in the row and column of 3

• By deleting the row and column of 3 and finding the determinant of the remaining 2x2 matrix

• By multiplying 3 with its adjacent elements

What is a cofactor in the context of a 3x3 matrix?

• The minor of the element multiplied by (-1) raised to the sum of its row and column indices

• The product of the element with its minor

• The average of all elements in the matrix

• The sum of all elements in the matrix

How is the cofactor of the element 3 calculated in the example?

• By adding all elements in the row and column of 3

• By multiplying the minor of 3 by (-1) raised to the sum of its row and column indices

• By subtracting the row and column sums from 3

• By dividing 3 by the sum of its row and column indices

What is the formula to find the determinant of a 3x3 matrix using cofactors?

• Difference between the sum of diagonal elements

• Sum of all elements in the matrix

• Product of all elements in the matrix

• Sum of products of elements of the first row with their corresponding cofactors

What is the determinant value of the given 3x3 matrix in the example?

• 54

• 38

• -54

• 0

What is the final determinant value for the 3x3 matrix discussed?

• -54

• 38

• 54

• 0