Determinant of a 3x3 Matrix Using the Diagonal Method

The video tutorial explains how to find the determinant of a 3x3 matrix using the diagonal method. It begins with setting up a 3x5 arrangement of elements from matrix A, then demonstrates the calculation of the determinant by summing the products of diagonals from the upper left to the lower right and subtracting the sum of products from the upper right to the lower left. The tutorial concludes with a discussion on singular matrices, explaining that a determinant of zero indicates a matrix is singular and non-invertible, while a non-zero determinant means the matrix has an inverse.

What is the first step in using the diagonal method to find the determinant of a 3x3 matrix?

• Find the inverse of the matrix.

• Form a 3x5 arrangement of elements.

• Calculate the sum of the diagonals.

• Subtract the products of the diagonals.

How are the fourth and fifth columns of the 3x5 arrangement determined?

• They are random values.

• They are the inverse of the first and second columns.

• They are the same as the first and second columns of the original matrix.

• They are the sum of the first and second columns.

What is the purpose of forming a 3x5 arrangement in the diagonal method?

• To find the inverse of the matrix.

• To prepare for calculating the determinant.

• To transpose the matrix.

• To simplify the matrix.

In the diagonal method, what is the first calculation step for finding the determinant?

• Transpose the matrix.

• Add the product of the blue diagonals.

• Subtract the sum of the red diagonals.

• Multiply all elements of the matrix.

What is the result of the calculation 2 x 6 x 1 in the diagonal method?

• 6

• 18

• 12

• 8

What is the next step after calculating the sum of the blue diagonals?

• Add the sum of the red diagonals.

• Subtract the sum of the red diagonals.

• Multiply the sum of the blue diagonals.

• Divide by the sum of the red diagonals.

What is the final determinant value calculated in the example?

• 0

• 49

• 20

• 29

What does it mean if a matrix is singular?

• It has a determinant greater than 1.

• It is invertible.

• It is a 2x2 matrix.

• It has a determinant of 0.

What is the implication of a matrix having a determinant of 0?

• The matrix is invertible.

• The matrix is diagonal.

• The matrix is singular and not invertible.

• The matrix is a 4x4 matrix.

If a matrix has a determinant of 49, what can be concluded?

• The matrix is a 2x2 matrix.

• The matrix has an inverse.

• The matrix is not invertible.

• The matrix is singular.