Let M = (u, v, w) be a 3 × 3 matrix.Pr ove that det(M) is equal to (u × v) · w

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Let M = (u, v, w) be a 3 × 3 matrix.Pr ove that det(M) is equal to (u × v) · w.Conc lude that M represents an orientation-preserving transformation if and only if det(M) > 0.Also , prove that if u and v are unit vectors that are orthogonal to each other, then setting w = u × v makes M = (u, v, w) a rigid, orientation-preserving transformation.

 

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