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SOLVED: (a) Prove that an orthogonal 2 Ã— 2 matrix must have the form [cos(Î¸) -sin(Î¸); sin(Î¸) cos(Î¸)], where Î¸ is a unit vector.(b) Using part (a), show that every orthogonal 2 Ã— 2 matrix is of the form [cos(Î¸) -sin(Î¸); sin(Î¸) cos(Î¸)], where 0 â‰¤ Î¸ â‰¤ 2Ï€.(c) Show that every orthogonal 2 Ã— 2 matrix corresponds to either a rotation or a reflection in 2.(d) Show that an orthogonal 2 Ã— 2 matrix Q corresponds to a rotation in R2 if det(Q) = 1 and a reflection in R2 if det(Q) = -1.

SOLVED: (a) Prove that an orthogonal 2 Ã— 2 matrix must have the form [cos(Î¸) -sin(Î¸); sin(Î¸) cos(Î¸)], where Î¸ is a unit vector.(b) Using part (a), show that every orthogonal 2 Ã— 2

VIDEO ANSWER: Hello there. So for this exercise we are going to prove that any 2x2 matrix that is orthogonal can be represented in only two ways. The first is …

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