Linear Algebra is strikingly similar to the algebra you learned in high school, except that in the place of ordinary single numbers, it deals with vectors.

Solution. We just multiply each entry by et: et cos t = sin t ing two vectors together. Let , w be two vectors in Rn. Then we can define th a1 b1 a1 + b1 ... = ...

Many concepts concerning vectors in Rn can be extended to other mathematical systems. We can think of a vector space in general, as a collection of objects that behave as vectors do in Rn. The objects …

In this section we will introduce the concepts of linear independence and basis for a vector space; but before doing so we must introduce some preliminary notation.

The following is a compact review of the primary concepts of linear algebra. The order of pre- sentation is unconventional, with emphasis on geometric intuition rather than mathematical formalism.

There are many other domains where linearity is important. For example, systems of linear algebraic equations and matrices. In this next unit on linear algebra we will study the common features of …

Together with matrix addition and multiplication by a scalar, this set is a vector space. Note that an easy way to visualize this is to take the matrix and view it as a vector of length m n. Not all spaces are …