Write down the dimensional matrix of MXN, where m is the number of rows and n is the number of columns of the object. In the most simple case of finding the sum of all matrix elements follow the sequence of addition of its values. The first line of the first element with the second fold to the obtained result, add a third etc. until the last row value. Further to the sum of the elements of the first row in the same way add the values of the second and all subsequent rows of the matrix. Moreover, when adding numbers, keep in mind their sign. So, the values of -4 and 5 give the sum of 1 and -5 + -6 = -11.
Determine the sum of the elements on the main diagonal of the matrix. The main diagonal of the matrix is from top left to bottom right. All items standing on the "straight" fold together. Determine the sum of all numbers on the main diagonal, record the final result.
Similarly calculate the sum of the elements on the secondary diagonal of the matrix in question. The secondary diagonal is called the "direct" passing from the upper-left corner of the matrix in the lower right. All values of the object lying on the diagonal, add together and record the result.
Find the sum of elements standing below the main diagonal. To do this, swipe on the main diagonal of the matrix line, shut-off values of the diagonal and the upper part of the object. Find the sum of the elements located below the straight line. For this purpose it is desirable to add the values line by line. From the first row below the main diagonal take the only one standing there element, fold it with the first element of the next line, then to the sum add the value of the second element. Next, go to elements in the third row, etc. until after adding the last cross out of the matrix element below the main diagonal.
To calculate the sum of matrix elements that stand above the main diagonal, and do the same, only in quality terms consider the elements stand above the crossed out diagonally.
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.