The number of columns and rows specify the dimension of the matrix. For example, table dimensionu 5×6 has 5 rows and 6 columns. In the General case, the dimension of the matrix written as m×n where the number m indicates the number of rows, n – columns.
The dimension of the matrix is important to consider when performing algebraic operations. For example, it is possible to put the matrices only of the same size. The operation of addition of matrices with different dimensionYu is not defined.
If the array has the dimension m×n can be multiplied by an array of n×l. The number of columns of the first matrix must equal the number of rows of the second, otherwise the multiplication is not defined.
The dimension of the matrix indicates the number of equations in the system and the number of variables. The number of rows equals the number of equations, and each column is fixed by a variable. Solution of system of linear equations "written" in the actions on matrices. Thanks to the matrix system of recording becomes possible to solve systems of high order.
If the number of rows equal to the number of columns, the matrix is called square. It is possible to distinguish the main and the secondary diagonal. Main goes from the upper left corner to the bottom right side from the upper right to the lower left.
Arrays dimensionu m×1 or 1×n are vectors. A vector can represent any row and any column of an arbitrary table. For such matrices defined all the operations on vectors.
Changing the matrix A, rows and columns sometimes, you can get the transpose of a matrix A(T). Thus, when transposing the dimension m×n will move to n×m.
The programming for rectangular tables you specify two indexes, one of which runs the length of the whole string, the other the entire length of the column. With loop for one index inside of the loop to the other, thereby providing a consistent through the entire dimension of the matrix.
Advice 2: How to solve matrix
A mathematical matrix is an organized table of elements. The dimension of the matrix is determined by the number of rows m and columns n. Under the decision matrix is understood as a set of generalized operations on matrices. There are several types of matrices, some of them are not applicable the number of operations. There is the operation of addition for matrices with the same dimension. The product of two matrices is only if they are coordinated. For any matrix is defined by determinants. Also a matrix can be transposed and to determine the minor elements.
Write down the given matrix. Determine the dimensionality. To do this, count the number of columns n and rows m. If for one matrix m = n, the matrix is considered to be square. If all the elements of the matrix equal to the zero matrix is zero. Define the main diagonal of the matrices. The switching elements are arranged from the upper left corner of the matrix to the bottom right. Second, the inverse of a diagonal matrix is a by.
Spend the transposition of a matrix. To do this, replace each matrix row elements on the column elements relative to the main diagonal. The element A21 will be the element A12 in the matrix and Vice versa. At the end of each of the source matrix get a new transposed matrix.
Fold the given matricesif they have the same dimension m x n. To do this, take the first element of the matrix A11 and fold it to the corresponding element b11 of the second matrix. The result of adding record in a new matrix at the same position. Then fold the elements A12 and b12 of both matrices. Thus complete all rows and columns summing matrix.
Determine whether the given matrix is consistent. To do this, compare the number of rows n in the first matrix and the number of columns m of the second matrix. If they are equal, perform the product of matrices. For this pairwise multiply each element of the row of the first matrix to the corresponding element in the column of the second matrix. Then find the sum of these products. Thus, the first element of the resulting matrix g11 = A11* b11 + A12*b21 + A13*b31 + ... + а1м*bn1. Perform the multiplication and addition of all works and fill in the result matrix G.
Find the determinant or determinants for any given matrix. For matrices of the second order - dimension 2 by 2 determinant is the difference of products of elements of main and secondary diagonals of the matrix. For the three-dimensional matrix formula of the determinant: D = A11* A22*A33 + A13* A21*A32 + A12* A23*A31 - A21* A12*A33 - A13* A22*A31 - A11* A32*A23.
To find the minor of a particular element of the zero matrix the row and column where is located this item. Then define the determinant of the obtained matrix. This will be a minor element.