3. (1 pt) Show that the matrix A below is orthogonal, and explain why it rotates the standard basis vectors (1,0) and (0

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3 1 Pt Show That The Matrix A Below Is Orthogonal And Explain Why It Rotates The Standard Basis Vectors 1 0 And 0 1 (36.69 KiB) Viewed 39 times

3. (1 pt) Show that the matrix A below is orthogonal, and explain why it rotates the standard basis vectors (1,0) and (0, 1) by an angle (Note that this implies that A as a linear transformation which preserves linear combinations must rotate all vectors u R² by an angle 9.) sin(0) A = (cos(0) sin(0) cos(0) 4. (1 pt) Let A be an n x n orthogonal matrix with real entries, and let u and v be vectors in R". Show that Au. Av=u. v. Why does this imply that u and Au have the same length?