A subspace V of ℝ n is called a hyperplane if V is defined by a homogeneous linear equation
c1x1 + c2x2 +· · ·+cn xn = 0,
where at least one of the coefficients ci is nonzero. What is the dimension of a hyperplane in ℝ n? Justify your answer carefully. What is a hyperplane in ℝ 3? What is it in ℝ 2?
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