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Q30Section II (Mathematics)30 of 190

Orthogonal complement of a subspace defined by two linear equations

Let W be the subspace of R4\mathbf R^4 given by W={(x1,x2,x3,x4)∣x1+2x2+3x3+4x4=0, x1−x2+x3=0}W=\{(x_1,x_2,x_3,x_4)\mid x_1+2x_2+3x_3+4x_4=0,\ x_1-x_2+x_3=0\}. Then W⊥W^\perp is generated by:

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