Calculating Determinants of Matrices

This video tutorial explains how to find the determinant of a 3x3 matrix. It begins with an introduction to the formula and arrangement of matrix elements. The tutorial then demonstrates how to calculate the determinant of a 2x2 matrix, which is a crucial step in the process. Two detailed examples are provided to illustrate the step-by-step calculation of a 3x3 matrix determinant. The video concludes with a summary and additional resources for further learning.

What is the first step in finding the determinant of a 3x3 matrix?

• Form 2x2 matrices by eliminating rows and columns

• Multiply all elements together

• Add all elements together

• Transpose the matrix

When forming a 2x2 matrix from a 3x3 matrix, what do you do with the row and column of the selected element?

• Add them together

• Transpose them

• Multiply them

• Eliminate them

How do you calculate the determinant of a 2x2 matrix?

• Add the diagonals

• Subtract the product of the diagonals

• Multiply the diagonals

• Divide the diagonals

In the first example, what is the determinant of the 3x3 matrix?

• 377

• -377

• 737

• -737

What operation is performed after calculating the determinants of the 2x2 matrices in a 3x3 matrix?

• Multiply them

• Subtract them

• Add them together

• Combine them with alternating signs

What is the importance of checking your work when calculating determinants?

• To ensure the matrix is correct

• To make the process faster

• To avoid mistakes that lead to incorrect answers

• To simplify the matrix

What should you do if you encounter two negative signs in a calculation?

• Multiply them

• Ignore them

• Add them

• Turn them into a positive sign

What is the first element used in the second example to find the determinant?

• 3

• 4

• 7

• 8

What is the result of 6 times -8 in the second example?

• 48

• -48

• -14

• 14

In the second example, what is the determinant of the 3x3 matrix?

• 717

• 177

• -177

• -717