Matrices are arrays of numbers or organized data. Operations with matrices include addition, subtraction, and multiplication. Matrices may also have inverses. The methods for finding the inverse of a matrix include using a formula, technology, or matrix operations. Matrices can represent systems of linear equations. A variety of techniques can be used to solve systems of equations represented as matrices.

At A Glance

  • Matrices of the same dimensions can be added or subtracted.
  • A scalar product is the product of a real number and a matrix.
  • An m×nm\times n matrix can be multiplied by an n×pn\times p matrix. The result is an m×pm\times p matrix.
  • If a matrix has an inverse, the product of the matrix and its inverse is the identity matrix.
  • There are different methods for determining the inverse of a matrix, including using an augmented matrix and row operations, using technology, and using a formula that includes calculating the reciprocal of the difference of the diagonals.
  • The inverse of a matrix can be used to solve a matrix equation of the form AX=BAX=B.
  • Gaussian elimination is a method of solving systems of linear equations by using an augmented matrix and row operations.
  • Row operations can be used to determine whether a linear system of equations is consistent and independent, inconsistent, or dependent.
  • The determinant of a square matrix is a value related to properties of the matrix.
  • Cramer's rule is a method of using determinants to solve systems of linear equations.