Linear Algebra is most often combined with another subject, such as Trigonometry, Mathematical Analysis, or Pre-Calculus. Students solve simultaneous linear equations in any number of variables using Gauss-Jordan elimination. Students interpret linear systems as coefficient matrices and the Gauss-Jordan method as row operations on the coefficient matrix. Students reduce rectangular matrices to row echelon form. Students perform addition on matrices and vectors.
Students perform matrix multiplication, multiply vectors by matrices and by scalars.
Students interpret the solution sets of systems of equations geometrically. For example the solution set of a single linear equation in two variables is interpreted as a line in the plane, and the solution set of a two by two system is interpreted as the intersection of a pair of lines in the plane. Students demonstrate understanding of the notion of the inverse to a square matrix, and apply it to solve systems of linear equations. Students know that a square matrix is invertible if, and only if, its determinant is non-zero. They can compute the inverse to 2 by 2 and 3 by 3 matrices using row reduction methods or Cramer's rule.