9.4 Matrix Operations

  • Add, subtract, and multiply matrices when possible.

  • Write a matrix equation equivalent to a system of equations.

In addition to solving systems of equations, matrices are useful in many other types of applications. In this section, we study matrices and some of their properties.

A capital letter is generally used to name a matrix, and lower-case letters with double subscripts generally denote its entries. For example, a47, read “a sub four seven,” indicates the entry in the fourth row and the seventh column. A general term is represented by aij. The notation aij indicates the entry in row i and column j. In general, we can write a matrix as

A=[aij]=[ a11a12a13a1na21a22a23a2na31a32a33a3nam1am2am3amn ].

The matrix ...

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