3Blue1Brown
The Determinant | Essence of Linear Algebra, Chapter 5
Determine how much a linear transformation alters area. The seventh segment in a series of 15 makes the connection between the determinant and the scale factor of areas during a linear transformation. The video goes on to explain the...
Brightstorm
Square Matrices - Concept
No, matrices are not what mathematicians sleep on. Lesson begins with identifying the dimensions of matrices then moves on to multiply them. It also provides guided practice problems that get progressively more complex.
Khan Academy
Khan Academy: Linear Algebra: Determinant When Row Multiplied by Scalar
An instructional video explaining what happens to the determinant when one row in a matrix is multiplied by a scalar. Proves that the new determinant will simply be the scalar times the original determinant. Also addresses the case when...
Khan Academy
Khan Academy: Linear Algebra: Determinant as Scaling Factor
Video demonstrating that the area of a parallelogram that is the image of a rectangle under a transformation is equivalent to the absolute value of the determinant of the matrix whose column vectors generate the parallelogram. Includes...
Khan Academy
Khan Academy: Linear Algebra: Duplicate Row Determinant
A video lesson proving that if a matrix has duplicate rows then its determinant will be 0. It follows then that such a matrix will not be invertible. [8:19]
Khan Academy
Khan Academy: Linear Algebra: Rule of Sarrus of Determinants
A video lesson presenting the Rule of Sarrus for finding the determinants of 3 x 3 matrices. The rule is derived algebraically and then used in a concrete example to find the determinant of a given 3 x 3 matrix. [7:18]
Khan Academy
Khan Academy: Linear Algebra: Determinant and Area of a Parallelogram
Video demonstrating that the area of a parallelogram created by graphing the column vectors of a 2x2 matrix is the equivalent to the absolute value of the determinant of the matrix. Pythagorean theorem, in conjunction with calculating a...
Khan Academy
Khan Academy: Linear Algebra: Determinant When Row Is Added
A video lesson explaining the determinant rule for the very special case when three matrices are identical except for one row, and that row of the third matrix is the sum of those rows in the other two matrices. Proves that the...
Khan Academy
Khan Academy: Linear Algebra: Upper Triangular Determinant
A video lesson proving that the determinant of an upper triangular matrix is the product of the all of the entries along the main diagonal. Includes a concrete example. [8:07]
Khan Academy
Khan Academy: Linear Algebra: (Correction) Scalar Multiplication of Row
A brief video correcting a notational mistake that was made in the previous video on how scalar multiplication affects the determinant. The formula in the previous video shows the entries being multiplied by the sub-matrices, when really...
Khan Academy
Khan Academy: Linear Algebra: Formula for 2 X 2 Inverse
A video lesson in which a formula is derived for finding the inverse of a 2 x 2 matrix. Addresses that a 2 x 2 matrix is only invertible if the determinant is not equal to 0. Defines the determinant and shows two examples of calculating...
Khan Academy
Khan Academy: Linear Algebra: Inverse Matrix (Part 1)
Video first explains and gives examples of identity matrices. Then explains what an inverse matrix is and shows how to calculate the inverse of a 2x2 matrix. [14:14]
Khan Academy
Khan Academy: More Determinant Depth: Determinant as Scaling Factor
Video demonstrating that the area of a parallelogram that is the image of a rectangle under a transformation is equivalent to the absolute value of the determinant of the matrix whose column vectors generate the parallelogram.
Khan Academy
Khan Academy: More Determinant Depth: Determinant When Row Is Added
A video lesson explaining the determinant rule for the very special case when three matrices are identical except for one row, and that row of the third matrix is the sum of those rows in the other two matrices.
Khan Academy
Khan Academy: More Determinant Depth: Upper Triangular Determinant
A video lesson proving that the determinant of an upper triangular matrix is the product of the all of the entries along the main diagonal
Khan Academy
Khan Academy: More Determinant Depth: (Correction) Scalar Multiplication of Row
Correction of last video showing that the determinant when one row is multiplied by a scalar is equal to the scalar times the determinant
Sophia Learning
Sophia: Minors: Lesson 5
This lesson defines minors and their relationship to determinants. It is 5 of 7 in the series titled "Minors."
Sophia Learning
Sophia: Minors: Lesson 6
This lesson defines minors and their relationship to determinants. It is 6 of 7 in the series titled "Minors."
Sophia Learning
Sophia: Minors: Lesson 1
This lesson defines minors and their relationship to determinants. It is 1 of 7 in the series titled "Minors."
Sophia Learning
Sophia: Sarrus' Rule: Lesson 5
This lesson introduces Sarrus' rule. It is 5 of 6 in the series titled "Sarrus' Rule."
Sophia Learning
Sophia: Sarrus' Rule: Lesson 1
This lesson introduces Sarrus' rule. It is 1 of 6 in the series titled "Sarrus' Rule."
Sophia Learning
Sophia: Using Determinants to Classify Systems of 3x3 Matrices
This lesson demonstrates how the determinant of a 3x3 matrix can be used to tell whether or not the matrix represents a dependent linear system, an inconsistent linear system, or neither.