Khan Academy: Linear Algebra: Determinant of a Transpose

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...

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...

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...

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...

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 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...

A video lesson proving that the product of a matrix and its transpose is invertible if all of the columns of the originial matrix are linearly independent. [12:34]

Video reviews from previous videos that a function is invertible if and only if it is onto and one-to-one. Shows how to determine if a linear transformation is onto by showing that the columns of the transformation matrix span the...

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]

A video lesson proving that the determinant of a matrix does not change even after performing row operations on the matrix. [10:25]