2. Let A = be an orthogonal 2 × 2 matrix. cos(0) sin(0 (a) Explain why the vector can be written as for some value of 0. a Use your answer to part (a) to find all 2×2 orthogonal matrices A = |C (b)...

2. Let A =<br>be an orthogonal 2 × 2 matrix.<br>cos(0)<br>sin(0<br>(a)<br>Explain why the vector<br>can be written as<br>for some value of 0.<br>a<br>Use your answer to part (a) to find all 2×2 orthogonal matrices A =<br>|C<br>(b)<br>(Hint: What can the second column of A look like?)<br>(c)<br>det(A) = 1? What kind of linear transformation do they correspond to? !<br>Given your answer to part (b), what are the 2 × 2 orthogonal matrices with<br>

Extracted text: 2. Let A = be an orthogonal 2 × 2 matrix. cos(0) sin(0 (a) Explain why the vector can be written as for some value of 0. a Use your answer to part (a) to find all 2×2 orthogonal matrices A = |C (b) (Hint: What can the second column of A look like?) (c) det(A) = 1? What kind of linear transformation do they correspond to? ! Given your answer to part (b), what are the 2 × 2 orthogonal matrices with

Jun 04, 2022

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2. Let A = be an orthogonal 2 × 2 matrix. cos(0) sin(0 (a) Explain why the vector can be written as for some value of 0. a Use your answer to part (a) to find all 2×2 orthogonal matrices A = |C (b)...

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