[MUSIC] A matrix is simply a rectangular array of numbers considered as one mathematical object. When there are m rows and n columns in the array, we have an m by n matrimx written as m times n. Matrices are denoted with a capital, bold letter. For example, the matrix A is m times n matrix. Therefore the matrix A is said to have order m times n. The numbers which form A are called its elements or entries. In particular, A denotes the element in the ith row and the jth column. For brevity, the m times n matrix, is often expressed as (aij) m x n. In case of the order m x n is either obvious or unimportant we can express the matrix in an even more simple way as (aij). If the matrix A has only one row or only one column, it's called a vector. We distinguish between a row vector, which has only one row and a column vector, which has only one column. Row or column vectors are denoted by small bold letters like x or y rather than capital letters. For example the matrix A is a 2 times 2 matrix, where A (1 1) = 2, A (1 2) = -4 A (2 1) = 8, A (2 2) = 1. B is local vector of 1 times 4, where B1,1 is equal to 2. B1, 2 is equal to the square root of 4. B1, 3 is equal to 2. B1, 4 is equal to 18. C is a column vector of 4 times 1. Where C1, 1 is equal to 7. C2, 1 is equal to 5. B3, 1 is equal to -1. B4, 1 is equal to 2. D is a 4 times 2 matrix with D1, 1 is equal to 2. D1, 2 is equal to 4. D 2, 1 is equal to 13. D 2, 2 is equal to 3. D 3, 1 is equal to 5. D 3, 2 is equal to 7. D 4, 1 is equal to 9. D 4, 2 is equal to 8. For example, construct the 4 times 3 matrix A, equal to aij, 4 times 3 with aij equal 3i minus j. The matrix has 12 entries 4 times 3, since 3i minus j. We have A (1 1) = 2, A (1 2) = 1, A (1 3) = 0, A (2 1) = 5, A (2 2) = 4 A (2 3) = 3. A (3 1) = 8. A (3 2) = 7. A (3 3) = 6. A (4 1) = 11. A (4 2) = 10. A (4 3) = 9. [MUSIC]