Matrices and Linear Equations
In Chapter 1, we mentioned the fact that a pair (x, y) of real numbers can be used to represent a point in the plane. In Chapter 6, we used such a pair to represent a complex number. This is an example of an important aspect of mathematics— a mathematical object may be interpreted in several different ways. Once we have studied the mathematical objects, we have information which is available in every interpretation.
In this chapter we introduce a new mathematical object—the matrix. An m × n matrix is a rectangular array of mn numbers. We can think of the matrix as consisting of m rows, each having n entries, or as n columns, each having m entries. For example,
is a 2 × 3 matrix. We regard a matrix as ...
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