Math Problem Statement

задача по линейной алгебре.даны векторы a1,v1,v2,v3.доказать что векторы v1,v2,v3 образуют базис и найти координаты вектора a в базисе v1,v2,v3 a=(-1;2;-3) v1=(1;2;1) v2=(0;1;-1) v3=(-1;2;1)

Solution

Решение задачи

Шаг 1. Проверим, образуют ли векторы (

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Vector Spaces
Basis and Coordinates

Formulas

Determinant of a matrix: det(A)
Coordinate transformation formula: a = c1*v1 + c2*v2 + c3*v3
Solving linear systems of equations

Theorems

Basis theorem: A set of n linearly independent vectors in an n-dimensional vector space forms a basis.
Linear independence: Determinant of a matrix formed by vectors is nonzero if they are linearly independent.

Suitable Grade Level

Undergraduate (Year 1-2)

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