Math 141-copyright Joe Kahlig, 10B                                                            Page 1
          Section 2.4: Introduction to Matrices
          Definition: A matrix is a rectangular array of numbers. The order or dimension of a matrix is
          m×nwhere m is the number of rows and n is the number of columns. The element in the ith row
          and the jth column of matrix A is denoted a     or A     =A . If the number of rows and columns
                                                       i;j     (i;j)   i;j
          are equal, then the matrix is called a square matrix.
          Example: Use these matrices in the following.
               " 3   2  1 #               1                h              i               1    3   0 
          A=                        B= 8              C= 0 2 5 6                    D= 4 10 7 
                 4   5  7                 4                                               5    2   6 
          A) Give the dimension of the above matrices.
          B) A    =                B =
               2;3                   2;1
          C) 4C    +2A −7D =
                1;3     1;2     2;2
          Definition: Scalar multiplication is multiplying a matrix by a constant.
          Example : If A= " 1    2   3 # and B = " 2     0  −3 #, compute
                              4  5   6               7   1   0
          2A=                                                −1B=
          Addition and Subtraction of Matrices: Two matrices of the same dimension can be added( or
          subtracted) by adding (or subtracting) corresponding entries.
          Example: Compute the following (if possible) with these matrices.
              " 1   2   3 #          " 2   0  −3 #             3 2              " 1   4  0 #
          A=                    B=                  ,    C= 1 6           D=
                4   5   6              7   1   0               0 5                2   3  8
          A) A+C =
          B) A+B=
         Math 141-copyright Joe Kahlig, 10B                                                          Page 2
         C) 3A+2B =
         D) D−B=
         E) 1:7A−3:1B +2:4D =
              T
         F) A =
         Example: Find a matrix J such that JT = J
         Example: Solve for x and y.
         3" 5 3 #+" 3          2x #T = " 18     −1 #
             y   7        −y −2            14   19