This video tutorial explains how to calculate determinants for 2x2 and 3x3 matrices. It begins with an introduction to determinants, showing how to compute them for 2x2 matrices using a simple formula. The tutorial then covers two methods for calculating determinants of 3x3 matrices: the diagonal method and the cofactor method. Each method is explained step-by-step, with examples to illustrate the process. The video emphasizes the importance of understanding these methods for solving matrix-related problems.

What is the determinant of a 2x2 matrix with elements a, b, c, and d?

• a - b + c - d

• a + d - b - c

• ad - bc

• ab + cd

What is the determinant of a 2x2 matrix with elements -8, 1, -3, and 9?

• 0

• 19

• 10

• 27

Which method involves copying columns to calculate a 3x3 determinant?

• Matrix Inversion Method

• Row Reduction Method

• Diagonal Method

• Cofactor Method

Tags

CCSS.HSN.VM.C.8

In the diagonal method, what do you do after copying the first two columns?

• Add them to the end of the matrix

• Subtract them from the matrix

• Ignore them

• Multiply them by the determinant

Tags

CCSS.HSN.VM.C.8

In the diagonal method, what is the result of the red diagonals?

• The product of the sums

• The quotient of the products

• The sum of the products

• The difference of the products

What is the determinant of a 3x3 matrix using the diagonal method if the red diagonals sum to 14 and the green diagonals sum to -4?

• 4

• 10

• 18

• 14

What is the first step in the method of cofactors?

• Copy the first row

• Add all elements together

• Multiply all elements by 2

• Select any row or column

How do you determine whether to add or subtract a product in the cofactor method?

• Randomly

• By the sum of the row and column indices

• Based on the size of the matrix

• By the determinant value

In the method of cofactors, what is the determinant of a 2x2 matrix formed by deleting a row and column?

• The sum of the elements

• The product of the diagonals

• The difference of the diagonals

• The sum of the diagonals

What is the final determinant of the 3x3 matrix using the method of cofactors in the example?

• 10

• 18

• 22

• 20