Find the standard matrix of the linear operator M: R2 R2 that first reflects every vector about the line y = x, then rotates each vector about the origin through an angle - ->> IC 3' and then finally dilates all the vectors with a factor of 3 2

Write down the 3 x 3 matrix that rotates a 2D point by angle about a point p = (xp, yp).

Let V₁, V2, V3 be the vectors in R³ defined by 18 ---D V₁ = -6 V2 = -14 V3 = 20 (a) is (V1, V2, Vs} linearly independent? Write all zeros if it is, or if it is linearly dependent write the zero vector as a non-trivial (not all zero coefficients) linear combination of V₁, V₂, and V3 0 (c) Type the dimension of span {V1, V2, V3}: Note: You can earn partial credit on this problem. -25 -18] 0=v₁+√₂+vs (b) Is (v1, vs} linearly Independent? Write all zeros if it is, or if it is linearly dependent write the zero vector as a non-trivial (not all zero coefficients) linear combination of V₁ and V3. 0=v₁+v₁ V3

Show the process of Reflecting a vector/matrix about a line that goes through the origin?