Arbitrary vector of any -dimensional space can be expressed in the form of the linear combination of some basis vectors of this -dimensional space. Such the decomposition is uniquely one.

*Decomposition*
of the arbitrary
-dimensional vector
in the
basis formed by linearly independent system of
-dimensional vectors
_{1} ,
_{2} , ... ,
_{n} ,
has the following form:

=
λ_{1}
_{1} +
λ_{2}
_{2} + ... +
λ_{n}
_{n}

, where
λ_{i} −
some constants called the coefficients of the decomposition (linear combination) of the vector
in basis
_{1} ,
_{2} , ... ,
_{n}.

Our online calculator is able to find the decomposition of vector in basis with step by step solution.

Decompose vector by basis

by:

= { }

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