# 16 Matrices; Systems of Linear Equations

# LEARNING OUTCOMES

After completion of this chapter, the student should be able to:

Add and subtract matrices

Multiply a matrix by a scalar

Perform matrix multiplication

Find the inverse of a matrix

Solve a system of linear equations by using the inverse of the matrix of coefficients

Solve a system of linear equations by using Gaussian elimination

Identify a system of linear equations as having a unique solution, no solution, or an unlimited number of solutions

Evaluate determinants of any order

Solve a system of linear equations by determinants

While working with systems of linear equations in the 1850s and 1860s, the English mathematician Arthur Cayley developed the use of a *matrix* (as we will show, ...

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