Virtually Passed
cross product moment example
Calculating the moment of a force can be quite tricky (especially in 3 dimensions). A good way to solve these problems is to use the cross product noting that *M* = *r* x *F*
Brian McLogan
Determining the Unit Vector in the Same Direction of a Vector
Learn how to determine the unit vector of a vector in the same direction. The unit vector is a vector that has a magnitude of 1. The unit vector is obtained by dividing the given vector by its magnitude.
Professor Dave Explains
Stokes's Theorem
Stokes's Theorem is kind of like Green's Theorem, whereby we can evaluate some multiple integral rather than a tricky line integral. This works for some surface integrals too. Let's see how it works!
msvgo
Evaluating Determinants
It explains how to evaluate the determinants of order 3 with the help of examples.
Virtually Passed
cross product and dot product summary
This is not a proof video, this video just describes the easiest way to solve for dot products and cross products.
msvgo
Properties of Determinants
It states and verifies different properties of determinants. Further illustrates each property through an example.
Professor Dave Explains
Solving Systems Using Cramer's Rule
How to solve systems of linear equations using Cramer's rule.
Tarver Academy
Finding the Determinant of a 3x3 Matrix
In This Episode, Tyler Teaches Us About Finding the Determinant of a 3x3 Matrix
Professor Dave Explains
Evaluating the Determinant of a Matrix
How to find the determinant of a matrix.
Khan Academy
Complex Determinant Example, Imaginary and Complex Numbers, Precalculus
Sal solves a complex determinant problem from the 2010 IIT entrance test. Knowledge of determinants, the exponential form of complex numbers, trigonometric ratios, and algebraic thinking are all utilized here.
Khan Academy
Khan Academy: Linear Algebra: 3 X 3 Determinant
A video lesson that shows how to find the determinant of a 3 x 3 matrix using cofactor expansion. Defines the formula in general terms then shows a concrete example. [10:01]
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: 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: N X N Determinant
An instructional video that gives a recursive definition for the determinant of an N x N matrix based on cofactor expansion. Uses the definition to find the determinant of a concrete 4 x 4 matrix. [18:40]
Khan Academy
Khan Academy: Linear Algebra: Determinant After Row Operations
A video lesson proving that the determinant of a matrix does not change even after performing row operations on the matrix. [10:25]
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: Determinants Along Other Rows/cols
A video lesson describing how the determinants for larger matrices can be found using cofactor expansion on any row or column. Illustrates that it is helpful to choose rows or columns with zeros in order to simplify the computations....
Khan Academy
Khan Academy: Linear Algebra: Simpler 4x4 Determinant
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]
Khan Academy
Khan Academy: Linear Algebra: Inverting Matrices (Part 2)
Video example of finding the inverse of a 3 by 3 matrix. Includes using expansion by minors to determine the determinant and finding the matrix of cofactors and adjugate or adjoint matrix. This video also appears in the strand Algebra:...
Khan Academy
Khan Academy: Linear Algebra: Singular Matrices
Video explains why a matrix is singular if its determinant is 0. Illustrates that when a matrix equation is built with a singular matrix, then there are no solutions because the system it represents is that of two parallel lines. Shows...
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...