Understanding Trace and Determinant of a 3x3 Matrix

This video tutorial explains how to find the trace and determinant of a 3x3 matrix using both formal definitions and eigenvalues. It covers the calculation of eigenvalues, the trace as the sum of diagonal elements or eigenvalues, and the determinant using both the cofactor method and the product of eigenvalues. The tutorial provides step-by-step guidance and examples to enhance understanding.

What is the primary focus of the video tutorial?

• Solving linear equations

• Finding the inverse of a matrix

• Understanding matrix multiplication

• Calculating the trace and determinant of a 3x3 matrix

What are the eigenvalues of the given 3x3 matrix?

• 1 and 3

• 2 and 4

• 3 and 5

• 4 and 6

What is the multiplicity of the eigenvalue 2 for the given matrix?

• 2

• 4

• 1

• 3

How is the trace of a matrix calculated using its diagonal elements?

• By dividing the diagonal elements

• By subtracting the diagonal elements

• By adding the diagonal elements

• By multiplying the diagonal elements

What is another method to find the trace of a matrix besides using diagonal elements?

• Using the quotient of eigenvalues

• Using the difference of eigenvalues

• Using the product of eigenvalues

• Using the sum of eigenvalues

Which of the following is true about the trace of a square matrix?

• It is equal to the sum of its eigenvalues

• It is equal to the product of its eigenvalues

• It is always zero

• It is always negative

Which method is NOT mentioned for calculating the determinant of a matrix?

• Diagonal method

• Cofactor method

• Using eigenvalues

• Row reduction method

What is the determinant of the given 3x3 matrix using the cofactor method?

• 20

• 16

• 12

• 8

How can the determinant of a matrix be calculated using eigenvalues?

• By adding the eigenvalues

• By multiplying the eigenvalues

• By subtracting the eigenvalues

• By dividing the eigenvalues

What is the product of the eigenvalues for the given matrix?

• 8

• 12

• 16

• 20