

Graphs Numbers 
MatricesThe matrices section of QuickMath allows you to perform arithmetic operations on matrices. Currently you can add or subtract matrices, multiply two matrices, multiply a matrix by a scalar and raise a matrix to any power. What is a matrix?A matrix is a rectangular array of elements (usually called scalars), which are set out in rows and columns. They have many uses in mathematics, including the transformation of coordinates and the solution of linear systems of equations. Here is an example of a 2x3 matrix : 1 2 3 4 5 6 ArithmeticThe arithmetic suite of commands allows you to add or subtract matrices, carry out matrix multiplication and scalar multiplication and raise a matrix to any power. Matrices are added to and subtracted from one another element by element. For instance, when adding two matrices A and B, the element at row i, column j of A is added to the element at row i, column j of B to give the element at row i, column j of the answer. Consequently, you can only add and subtract matrices which are the same size. Matrix multiplication is a little more complicated. Suppose two matrices A and B are multiplied together to get a third matrix C. The element at row i, column j in C is found by taking row i from A and multiplying it by column j from B. Two matrices can only be multiplied together if the number of columns in the first equals the number of rows in the second. Multiplying a matrix by a scalar simply involves multiplying each element by that scalar, whilst raising a matrix to a positive integer power can be achieved by a series of matrix multiplications. There is currently no advanced arithmetic section, though this may be introduced in the future. InverseThe inverse command allows you to find the inverse of any nonsingular, square matrix. The inverse of a square matrix A is another matrix B of the same size such that A B = B A = I where I is the identity matrix. The inverse of A is commonly written as A^{1}.DeterminantThe determinant command allows you to find the determinant of any nonsingular, square matrix. For example, if A is a 3 x 3 matrix, then its determinant can be found as follows : det(A) = a_{1,1} A_{1,1}  a_{1,2} A_{1,2} + a_{1,3} A_{1,3} where a_{i,j} is the element of A at row i, column j and A_{i,j} is the matrix constructed from A by removing row i and column j. Introduction to Matrices and Systems of Equations
Consider the system We adopt a convention here of using subscripted variables rather than individual letter variables to avoid possible difficulties in the number of available letters. We construct a 2 x 3 matrix, called the augmented matrix for the system, where each row represents information for a particular equation and each column represents either coefficients of a variable or the constants on the righthand side of the equations. We write this matrix as follows.
Performing any sequence of these operations results in a rowequivalent
matrix.
