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Examples of solvings

  • Compute the determinant:

    • a) by expanding along the i-th row;
    • b) by expanding down the j-th column;
    • c) first obtaining zeros in the i-th row.
    | 1134 2008 3002 4475 | , i = 1 , j = 2 ;
    For a solution you could use the page "Determinant calculator":
    • a) You should enter in the input field near the button "Expand along the row" the row number - 1. Then click this button. The solution will appear below.
    • b) You should enter in the input field near the button "Expand along the column" the column number - 2. Then click this button. The solution will appear below.
    • c) You should enter in the input field near the button "Get zeros in the row" the row number - 1. Then click this button. The solution will appear below.
  • Evaluate a matrix expression to find the matrix K:

    K = 3⁢A⁢B − 2⁢C⁢D ,
    A = ( 120 −1−34 25−6 ) , B = ( 136−7 20−1−3 0245 ) , C = ( 43 −20 14 ) , D = ( 2−130 0235 ) ;
    To find the solution it is possible to use the page "Matrix calculator":
    1. Find on the page a button which adds matrix input tables, press it two times to get the input fields for matrices C and D.
    2. Enter the matrix A into the table "Matrix A", the matrix B into the table "Matrix B", the matrix C into the table "Matrix C", the matrix D into the table "Matrix D".
    3. Then enter the expression 3AB-2CD into the expression input field and press the button "=" next to the field.
    4. The result will appear below on the page.
  • A problem. The enterprise lets out three kinds of production, using raw material of three types. Charges of each type of raw material by kinds of production and stocks of raw material at the enterprise are given in the table. To define volume of output of each kind at the set stocks of raw material.

    Type of raw materialCharge of raw material by kinds of production, weight/num.Stock of raw material, weight units
    123
    I2351030
    II321620
    III113510
    Let's make a system of the equations:
    2x_1 + 3x_2 + 5x_3 = 1030
    3x_1 + 2x_2 + 1x_3 = 620
    1x_1 + 1x_2 + 3x_3 = 510
    Let's use the page "System of equations calculator" to find the solution:
    1. Put the coefficients of the system into the input fields.
    2. Then press the button "Solve by Cramer's rule."
    System of equations calculator
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☕ Support
Thanks to:
  • Philip Petrov (https://cphpvb.net) for Bulgarian translation
  • Manuel Rial Costa for Galego translation
  • Shio Kun for Chinese translation
  • Petar Sokoloski for Macedonian translation
  • Duy Thúc Trần for Vietnamese translation
  • Rıfkı Kürşat Vuruşan for Turkish translation
  • Ousama Malouf and Yaseen Ibrahim for Arabic translation
  • Marcel Artz - improving of the German translation
  • Marc Gisbert Juàrez - fixing the translation into Catalan