Khan Academy
Khan Academy: Algebra: Complex Numbers: Iit Jee Complex Numbers (Part 3)
Video shows working a problem from the IIT JEE test which involves determining whether the determinant of a matrix of four given complex numbers is 0. [3:09]
Khan Academy
Khan Academy: Pre Calculus: Basic Complex Analysis
A video [13:04] introducing complex analysis. Complex numbers are defined as a number having two parts: a real part and an imaginary part. The instructor shows how to graph these in the complex number plane. The video also explains how...
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Khan Academy: Differential Equations: Laplace Transform 6
Video uses the properties of the Laplace transform shown in the previous video and extends them to show how they can be used to simplify problems and help find values for the Laplace transform table more quickly. Examples include trig...
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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...
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Khan Academy: Linear Algebra: Vector Transformations
Video first reviews the meaning of functions and talks about functions mapping sets from R^n to R^m. Gives examples of writing functions in vector notation. Explains that in linear algebra a transformation is just a function operation on...
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Khan Academy: Statistics: Regression Line Example
Video demonstrates how to use the formulas to determine the best fitting regression line by doing an example of finding the regression line given 3 points. Includes graphing the regression line to show it visually. [9:27]
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Khan Academy: Geometry: Proof Rhombus Diagonals Are Perpendicular Bisectors
Demonstrates how to prove that the diagonals of a rhombus are perpendicular bisectors of each other based on knowledge of properties of parallelogram diagonals, triangle congruency, and supplementary angles. [4:04]
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Khan Academy: Linear Algebra: Using Orthogonal Change of Basis Matrix Example
Video defining an orthogonal matrix as a square matrix C whose columns form an orthonormal set. Shows that C will be invertible and that multiplying C transpose by C will result in the identity matrix. The result that C transpose equals...
Khan Academy
Khan Academy: Differential Equations: Laplace Transform 3 (L{sin(at)})
Video first reviews integration by parts then shows finding a Laplace transform table value using integration by parts twice. Problem is continued in next video. [10:44]
Khan Academy
Khan Academy: Algebra: Factoring Trinomials With a Common Factor
Video demonstrates how to factor a trinomial with a leading coefficient of 8 and GCF of 8. Factor by grouping method is used to factor the trinomial. Practice problems available. [5:01]
Khan Academy
Khan Academy: Algebra: Application Problems Involving Units of Weight
A step-by-step breakdown on how to approach and solve a problem involving weight and converting between units. [7:08]
Khan Academy
Khan Academy: Algebra: Find an Unknown in a Proportion
Video demonstrates how to find an unknown in a proportion three different ways including algebraically with cross multiplication. This video also appears in the strand Arithmetic and Pre-Algebra: Ratios and Proportions. [7:20]
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Khan Academy: Linear Algebra: Normal Vector From Plane Equation
Video finding the normal vector to a plane using its equation by first visualizing the vector and the plane and then solving for it. Shows how to find the equation of a plane given the position vectors of two points on the plane and...
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Khan Academy: Linear Algebra: Visualizations of Left Nullspace and Rowspace
Video builds upon the column spaces and null spaces of the 2x3 matrix and its transpose found in the previous video. Uses them to explain some relationships between the four fundamental subspaces, namely that the orthogonal complement of...
Khan Academy
Khan Academy: Algebra: How to Rationalize a Denominator
Video working through multiple examples of rationalizing the denominator. Includes some examples with using the conjugate of the denominator as well as an example with variables. Video is also included in the Algebra: ck12.org strand....
Khan Academy
Khan Academy: Probability: Mega Millions Jackpot Probability
Video lesson solving for the probability of winning the mega millions jackpot. [5:29]
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: Geometry: Ca Geometry: Triangles and Parallelograms
In this video lesson [11:14], the instructor demonstrates solutions to problems #21-25 of California Geometry released state test questions. Problems address understanding of the triangle inequality theorem, angle relationships with...
Khan Academy
Khan Academy: Algebra: Special Polynomials Products 1
Video illustrates the pattern of multiplying binomials of the form (a + b)(a - b). Applies the pattern to multiply (2x + 8)(2x -8). [2:29]
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: Calculus: 2011 Calculus Ab Free Response #5B
Video shows how to find the second derivative of a function and use it to determine if the answer found in the previous video which used the slope of the tangent line is an underestimate or overestimate. [8:18]
Khan Academy
Khan Academy: Differential Equations: Undetermined Coefficients 2
Video shows an example of solving a second order linear nonhomogeneous differential equation involving trig functions using undetermined coefficients. [11:00]
Khan Academy
Khan Academy: Algebra: Addition Elimination Method 2
This video demonstrates how to solve a system of linear equations using the linear combination and elimination method. [4:25]
Khan Academy
Khan Academy: Algebra: Solving Systems by Substitution 1
This video demonstrates how to solve a system of linear equations by substitution. The sample problem given has no solution. [3:44]