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The full lesson and more can be found on our website at mathsathome.com/linear-programming In this lesson we look at an example of linear programming in which there are multiple optimal solutions. If two vertices optimise the objective function, then both of these vertices are optimal solutions. Furthermore, all points between these vertices are also optimal solutions.

The full lesson and more can be found on our website at mathsathome.com/linear-programming. Learn how linear programming problems can have multiple and infinite optimal solutions. Infinite solutions are produced when non-integer solutions are allowed and when multiple solutions exist.

The full lesson and more can be found on our website at mathsathome.com/linear-programming In this video, we learn how to do the linear programming process to find an optimal solution. We look at examples of maximising an objective function and minimising an objective function. We learn how to form constraint equations in the linear programming process and we learn how to graph constraint equat...

The full lesson and more can be found on our website at mathsathome.com/collinear-points/ In this lesson we learn what collinear means, what collinear points are and how to determine if three points are collinear. We look at examples of showing that three points are collinear using vectors.

The full lesson and more can be found on our website at mathsathome.com/mathematical-induction-products/ In this lesson, we learn how to do mathematical induction for problems involving products. We learn how to use the pi product notation to represent mathematical induction problems.

The full lesson and more can be found on our website at mathsathome.com/convert-degrees-minutes-seconds/ In this lesson we learn how to convert degrees, minutes and seconds to decimal degrees and how to read degrees, minutes seconds. We also learn how to convert decimal degrees to degrees, minutes and seconds.

The full lesson and more can be found on our website at mathsathome.com/vector-projections/ In this lesson we learn what the vector projection means and how to calculate the vector projection of one vector on another. We look at examples of questions involving vector projection in 2D and 3D.

The full lesson and more can be found on our website at mathsathome.com/scalar-product-vectors/ In this lesson we learn how to calculate the scalar product (also known as the dot product) for two vectors. We learn the formula for the dot product and use it to calculate the dot product for vectors in 2D and vectors in 3D.

The full lesson and more can be found on our website at mathsathome.com/inverse-2x2-matrix/ In this lesson we learn the formula for finding the inverse of a 2x2 matrix. We consider examples of calculating the inverse of 2x2 matrices and also discover how to decide if a matrix has an inverse or not.

The full lesson and more can be found on our website at mathsathome.com/equation-parallel-line-through-point/ In this lesson we learn how to find the equation of a parallel line passing through a given point. We look at several examples of calculating lines parallel to given lines in which they must pass through a particular coordinate.

The full lesson and more can be found on our website at mathsathome.com/angle-slope-line In this lesson we learn how to calculate the angle of a line when given its slope and also how to calculate the slope of a line when given its angle of inclination. The equation m = tanθ is used to convert the angle of a line into its slope on a cartesian plane and in this video we look at various examples ...

The full lesson and more can be found on our website at mathsathome.com/equation-line-2-points/(opens in a new tab) In this lesson we learn how to calculate the equation of a line passing through two given points. We calculate the gradient of the line from two points and then use this to form the slope-intercept form of the straight line equation.

The full lesson and more can be found on our website at mathsathome.com/trigonometry-angles In this lesson we learn how to find missing angles in a right-angled triangle using trigonometry. We use the formulae for sin, cos and tan in three examples of finding missing angles.

The full lesson and more can be found on our website at mathsathome.com/residual-plots Here we learn what a residual plot is and how to make them. We look at two examples of making residual plots following linear regression. In these two examples, we interpret the residual plot to decide if the model used is a good or bad fit for the data.

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