Determinants of Matrices

Professor Dave explains how to find the determinant of square matrices, starting with a 2x2 matrix and progressing to larger matrices. He details the algorithm for calculating determinants, using examples to illustrate the process. The video covers the step-by-step method for 3x3 matrices and discusses the approach for even larger matrices, emphasizing the importance of organization and arithmetic accuracy.

What is a square matrix?

• A matrix with more rows than columns

• A matrix with more columns than rows

• A matrix with only one row

• A matrix with an equal number of rows and columns

What is the determinant of a 2x2 matrix with entries A, B, C, and D?

• AC - BD

• AB + CD

• AD - BC

• A + B - C + D

For a 2x2 matrix with entries 2, 1, -6, and 4, what is the determinant?

• 12

• 10

• 14

• 16

What is the determinant of a 2x2 matrix with entries 3, 5, 7, and 9?

• -12

• 12

• 6

• -6

What is the determinant of a 2x2 matrix with entries 4, 3, 2, and 1?

• 10

• -10

• -2

• 2

What is the determinant of a 2x2 matrix with entries 0, 1, 2, and 3?

• -6

• -3

• 3

• 6

What is the determinant of a 2x2 matrix with entries 5, 6, 7, and 8?

• -4

• 2

• -2

• 4

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

• Break it down into a series of 2x2 determinants

• Add all entries together

• Subtract all entries

• Multiply all entries together

When calculating the determinant of a 3x3 matrix, what is done after selecting the first entry?

• Multiply it by the sum of all other entries

• Subtract it from the determinant of the remaining matrix

• Add it to the determinant of the remaining matrix

• Ignore its row and column and find the determinant of the remaining 2x2 matrix

In a 3x3 matrix determinant calculation, what is the sign pattern used?

• All negative

• Alternating positive and negative

• No specific pattern

• All positive