Online calculator. Decomposition of the vector in the basis

Guide - Decompose the vector in the basis calculator

• To decompose the vector in the basis:
• select the vectors dimension (the number of coordinates in a vector);
• enter the values of basis vectors;
• enter the vectors which you want to decompose in the basis;
• Press the button "Decompose the vector in the basis" and you will have a detailed step-by-step solution..

Entering data into calculator

You can input only integer numbers or fractions in this online calculator. More in-depth information read at these rules.

Additional features of the calculator

• You can navigate between the input fields by pressing the keys "left" and "right" on the keyboard.

a₁, ..., a_n with coefficients x₁, ..., x_n is a vector

x₁a₁ + ... + x_na_n.

To decomposition, the vector b on the basis vectors a₁, ..., a_n, you must find the coefficients x₁, ..., x_n, for which a linear combination of vectors a₁, ..., a_n is equal to vector b.

x₁a₁ + ... + x_na_n = b.

The coefficients x₁, ..., x_n are called the coordinates of the vector b in the basis a₁, ..., a_n.