Khan Academy: Linear Algebra: Duplicate Row Determinant

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...

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]

Video starts with reviewing matrix notation. Defines multiplying a matrix by a vector and shows examples. Shows how the matrix-vector products can be interpreted as the dot product of column vectors with a matrix or as a weighted linear...

Video first gives the conditions that define a linear transformation. Gives examples of determining if a transformation is linear or not. Shows several types of notation for vector transformations. [13:52]

Video shows another example of using matrices and reduced row echelon form to simplify a system of 3 equations in 4 variables. Explains how to determine how many solutions the system will have by looking at the reduced row echelon form....

Video demonstrating how to find the determinant of a 4x4 matrix by using row operations and row replacements to get the matrix into upper triangular form. [9:13]

Video shows how to use matrices and reduced row echelon form to simplify a system of 3 equations in 4 variables. Shows how the system relates to vectors to help visualize what the solution represents. This video also appears in the...

Video shows example of using matrices and reduced row echelon form to solve a system of 3 equations in 3 variables. This video also appears in the strand Algebra: Matrices. [7:37]

Video shows example of using matrices and reduced row echelon form to solve a system of 3 equations in 3 variables. This video also appears in the strand Algebra: Matrices. [7:37]

A video lesson proving that there is a unique solution in the row space of A to the equation Ax = b, where A is some m x n matrix, b is a vector that is a particular member of the column space of A, and x is a member of Rn. The solution...