Instruction

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The number of columns and rows specify

**the dimension****of the matrix**. For example, table**dimension**u 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.2

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**dimension**Yu is not defined.3

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.4

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.5

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.

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Arrays

**dimension**u 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.7

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.8

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.Instruction

1

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.2

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.3

Fold the given

**matrices**if 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**.4

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.5

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*A23.6

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.