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Q26Section ST (Statistics (Q11–Q65))26 of 65

Dimension of an orthogonal complement

Consider the subspace U={(x1,x2,x3,x4)∈R4:x1+x2+x4=0,  x3=0}U = \{(x_1, x_2, x_3, x_4) \in \mathbb{R}^4 : x_1 + x_2 + x_4 = 0, \; x_3 = 0\}. Let U⊥U^{\perp} be its orthogonal complement. The value of dim⁡(U⊥)\dim(U^{\perp}) equals ________ (answer in integer).

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