Math Problem Statement

Find the basis and dimension of the subspace V = {x = (x1, x2, x3, x4) ∈ ℝ^4 | x1 + 2x2 - x3 = 4x4}.

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Vector Spaces
Basis and Dimension

Formulas

General form of a vector in a subspace satisfying Ax = b
Basis determination: Independent vectors spanning the subspace

Theorems

Dimension theorem of vector spaces

Suitable Grade Level

University level

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