Matrix Operations

Free powerpoints at http://www.worldofteaching.com MATRIX: A rectangular arrangement of numbers in rows and columns. The ORDER of a matrix is the number of the rows and columns. The ENTRIES are the numbers in the matrix. rows This order of this matrix is a 2 x 3. columns  6 2  1  2 0 5    8 0   10   2 1  7  1 0 4 0 1 3 3 2   3  4 2 6 7 3x3 (or square matrix) 9 5 7 1x4 0 (Also called a column matrix) 5 9 3 8  6  3x5 1 0   1  2  9 7    0   6 4x1 (Also called a row matrix) 2x2 (or square matrix) To add two matrices, they must have the same order. To add, you simply add corresponding entries.  5  3   0   3   2 4  3   7   4   1  0    3  5  (2)  3  1   33   40   04 7  (3)    3  0   4   2 4   4    8 0 1 3   1 7  5 4 2 9    5 3    5 2 3  2  = =   8  (1) 07 4 3 1 5 2 3 3 2 9  (2)  5 5  7 0 7 7 4 5 5 7  To subtract two matrices, they must have the same order. You simply subtract corresponding entries.  9 2 4   4 0 7   9 4  5 0 6    1 5  4        5 1  1 3 8   2 3 2  1  (2)       5  4   3  20 05 33 2 5 0 47   6  (4) 82    3  10  6   =  2 8  1  2-0 8-3 1-(-4) 4 0 5 -4-1 5-2 3 0 1    3 1  7  0   4 2   3-8 0-7 0-(-1) -7-1  = 8  1 7  2 -5 -5 5 1 -8 5 3 -7  In matrix algebra, a real number is often called a SCALAR. To multiply a matrix by a scalar, you multiply each entry in the matrix by that scalar.  2 4  4 0  4(2)    1  4(4)  8   16 4(0)   4(1)  0    4  1  2   0   2   4  6 3   5     8   1 4  2   06  -2     -3 3 6 -5   2  5    3  (8)  -2(-3) -2(3) -2(6) -2(-5)    6 -6 -12 10 