**Topic: **Matrices. Cramer's Rule and Transformations in R^{2}

**When:** Friday, March 12 @ 11:00am

**Who:** Professor Dan Balaguy

**Where: **Canvas (https://sierra.instructure.com/courses/347458)

A major application of matrices is to represent linear transformations (that is, generalizations of linear functions such as *f*(*x*) = 4*x*). For example, the rotation of vectors in three-dimensional space is a linear transformation, which can be represented by a rotation matrix **R**: if **v** is a column vector (a matrix with only one column) describing the position of a point in space, the product **Rv** is a column vector describing the position of that point after a rotation. The product of two transformation matrices is a matrix that represents the composition of two transformations. Another application of matrices is in the solution of systems of linear equations.