MATRICES AND DETERMINANTS Higher Concepts of Mathematics Multiplication of a Matrix by a Matrix To multiply two matrices, the first matrix must have the same number of rows (m) as the second matrix has columns (n).  In other words, m of the first matrix must equal n of the second matrix. For example, a 2 x 1 matrix can be multiplied by a 1 x 2 matrix, x y a   b ax    bx ay    by or a 2 x 2 matrix can be multiplied by a 2 x 2.   If an  m x  n  matrix is multiplied by an n  x  p matrix, then the resulting matrix is an  m x  p matrix.   For example, if a 2 x 1 and a 1 x 2 are multiplied, the result will be a 2 x 2.   If a 2 x 2 and a 2 x 2 are multiplied, the result will be a 2 x 2. To multiply two matrices, the following pattern is used: A a   b c   d B w   x y   z C A B aw  by   ax  bz cw  dy   cx   dz In general terms, a matrix C which is a product of two matrices, A and B, will have elements given by the following. c_ij = a_i1b_1j + a_j2b_2j + + + . . . + a_inb_nj where i = ith row j = jth column Example: Multiply the matrices A x B. A 1 2 3 4 B 3 5 0 6 MA-05 Page 20 Rev. 0