Math Problem Statement

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

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Subspaces
Basis
Dimension

Formulas

Definition of subspaces in R^n
Dimension formula: Dimension = number of basis vectors
Gaussian elimination to find the basis

Theorems

Rank-Nullity Theorem

Suitable Grade Level

Undergraduate - Linear Algebra