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Introduction and Summary

Matrices and Matrix Addition

Dimensions  -  The number of rows and the number of columns in a matrix. For example, a 3×4 -dimensional matrix has 3 rows and 4 columns.
Elementary Row Operations  -  There are three elementary row operations:
  • Multiplying a row by a constant.
  • Switching two rows.
  • Adding a constant times a row to another row.
Identity Matrix  -  The matrix

I =    

Which, when multiplied by any matrix, does not change the matrix. In other words, any matrix multiplied by I is equal to itself.
Matrix  -  A way of representing data in a rectangular array.

A =    

Reduced Row-Echelon Form  -  The form of a matrix in which the first m×m entries form the identity matrix:


Row Reduction  -  The process through which a matrix is converted to reduced row-echelon form, using elementary row operations.
Scalar  -  A single constant, variable, or expression.