Khan Academy: Linear Algebra: Exploring the Solution Set of Ax=b

Sal dissects basic algebraic equations of the form Ax=B. He encourages viewers to fully understand the equations before learning how to manipulate them. Furthermore, he teaches students how to solve the equations systematically. The...

An instructional video that gives an example of how to find a solution to the equation Ax = b. In the example, the matrix A is 2 x 2. Shows that when the solution is a member of the row space of A for a given vector b, a member of the...

Given a replacement set of values, plug them in to find a solution set to this inequality expression.

A solution set is the set of ordered pairs that are the solutions to a two variable problem. Not sure what all that means? Watch this video and the teacher will explain it clearly.

Use a table to find the solution set for an equation. Watch an instructor as she directs how to create ordered pairs using a given domain and check your answers using one of these ordered pairs. A practical video for anyone, student or...

Use a table to find the solution set for an equation. Watch an instructor as she directs how to create ordered pairs using a given domain and check your answers using one of these ordered pairs. A practical video for anyone, student or...

Video first reviews what it means for a function to be invertible. Shows that if a function is invertible then there is a unique solution to f(x) = y. Also shows that if there is a unique solution to the equation f(x) = y for all y then...

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]

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...