12.2 SystemsLinearEqMatrices - bar appear at the bottom If...

12.2 Systems of Linear Equations: Matrices
A matrix is a rectangular array of numbers. Each number a
ij
of the matrix has to indices (subscripts), the
row index i and the column index j (see your book for an illustration). A matrix can be used to represent a
system of linear equations. If the constants to the right of the equal sign are included, it is called an
augmented matrix ; if the constants are not included, it is called a coefficient matrix . To solve a system,
there are three basic row operations : [1] Interchange any two rows; [2] replace a row by a nonzero multiple
of that row; and [3] replace a row by the sum of that row and a constant nonzero multiple of another row.
The goal is to get the matrix in row echelon form , which means [1] entry a
11
is a 1 and only zeros appear
below it; [2] the first nonzero entry in each subsequent row is a 1 with zeros below it and it is to the right of
the first nonzero entry in any row above it; and [3] any row that contains all zeros to the left of the vertical