Linear Algebra Example Problems - Coordinate System Representation Example #2

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When working with vectors we often implicitly use the standard basis. For example, the vector x = [2; -3] tells us the coordinates with respect to the standard basis {[1; 0], [0; 1]}.

At other times it is desirable to work with different coordinate systems that are represented by a different basis. We denote the vector x with respect to the basis B as [x]B.

In this problem we're provided a basis B and the vector x. We then compute the vector [x]B, the coordinates of x with respect to the basis B. We see that the coordinates of x with respect to the basis B can be computed easily by simply constructing and solving a system of linear equations.

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