Understanding Determinants

What is a square matrix?

• A matrix with the same number of rows and columns

• A matrix with more rows than columns

• A matrix with only one row

• A matrix with more columns than rows

Which notation is commonly used for the determinant of a matrix?

• sum(A)

• prod(A)

• det(A)

• abs(A)

How is the determinant of a 2x2 matrix calculated?

• By subtracting the product of one diagonal from the other

• By adding all elements together

• By adding the products of the diagonals

• By multiplying all elements together

What is the determinant of the matrix B if B = [[3, 4], [1, -5]]?

• -19

• 19

• -11

• 11

What is the determinant of matrix C if C = [[-2, 1], [3, -2]]?

• -2

• -4

• 2

• 4

What is the first step in finding the determinant of a 3x3 matrix using the column copying method?

• Multiply all elements of the matrix

• Copy the first two columns to the right of the matrix

• Add all elements of the matrix

• Subtract the first row from the last row

In the 3x3 determinant method, what do you do after copying the columns?

• Multiply the diagonals and subtract the results

• Add the copied columns to the original matrix

• Transpose the matrix

• Divide the matrix by the number of columns

What is the determinant of a 3x3 matrix if the sum of the left diagonals is -20 and the right diagonals is -30?

• 50

• -50

• -10

• 10

What is the purpose of using parentheses in the 3x3 determinant calculation?

• To multiply the diagonals

• To add clarity to the subtraction process

• To divide the matrix into sections

• To transpose the matrix

What is an alternative method for finding determinants of larger matrices?

• Matrix inversion

• Row reduction

• Cofactor expansion

• Gaussian elimination