Determinants of 3x3 Matrices

The video tutorial explains how to find the determinant of a 3x3 matrix using the diagonal method. It begins with setting up the matrix and adding two columns to facilitate the calculation. The process involves calculating the product of the down diagonals and the up diagonals separately. Finally, the sums of these products are subtracted to determine the matrix's determinant.

What method is used to find the determinant of a 3x3 matrix in this tutorial?

• Cofactor expansion

• Diagonal method

• Matrix inversion

• Row reduction method

How many columns are added to the back of the original matrix setup?

• None

• Three

• Two

• One

What is the first step in calculating the product of the down diagonals?

• Start at the bottom right corner

• Start at the top left corner

• Multiply the middle row

• Add all elements

What is the product of the first down diagonal in the example?

• Positive 2

• Negative 2

• Negative 6

• Zero

What is the sum of the products of the down diagonals?

• 70

• 72

• 68

• 66

Where do you start when calculating the product of the up diagonals?

• Middle of the matrix

• Bottom left corner

• Top right corner

• Top left corner

What is the sum of the products of the up diagonals?

• Positive 8

• Positive 16

• Negative 8

• Negative 16

What operation is performed to find the final determinant?

• Add the sums of the diagonals

• Subtract the sum of up diagonals from down diagonals

• Divide the sums of the diagonals

• Multiply the sums of the diagonals

What is the final determinant of the matrix in the example?

• 66

• 74

• 72

• 70

What does subtracting a negative number effectively do in the final calculation?

• It multiplies the number

• It divides the number

• It subtracts the number

• It adds the number