Understanding Adjoint and Inverse of a Matrix

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

• Compute the eigenvalues of the matrix

• Determine the matrix of co-factors

• Find the transpose of the matrix

• Calculate the inverse of the matrix

How do you determine the sign of a co-factor?

• By calculating the determinant of the entire matrix

• By adding the row and column indices and checking if the sum is odd or even

• By checking if the column number is odd

• By checking if the row number is even

What is the result of transposing the matrix of co-factors?

• The adjoint of the original matrix

• The determinant of the original matrix

• The inverse of the original matrix

• The identity matrix

Which method is used to find the determinant in the final section?

• Gaussian elimination

• Row reduction

• Matrix multiplication

• Co-factor expansion

What is the determinant of the matrix as calculated in the video?

• 6

• -6

• 0

• 1