- B 8 Points Find The Matrix Representation Of The Transformation F R3 R3 With Respect To The Standard Basis For R3 1 (115.52 KiB) Viewed 25 times
- B 8 Points Find The Matrix Representation Of The Transformation F R3 R3 With Respect To The Standard Basis For R3 2 (241.52 KiB) Viewed 25 times
(b) [8 points) Find the matrix representation of the transformation f : R3 R3 with respect to the standard basis for R3, i.e., find the matrix A E R3*3 such that f(x) Ax for all x € R3. Equivalently, find the matrix A = [ ui | u2 | u3 ), whose columns are given by ui = f(ei), u2 = f(en), uz = f(ez), where ez = [1,0,0], ez = [0,1,0]T, ez = [0,0,1]". (c) [6 points] Consider again the matrix A that was defined in Part (b). Determine the null space and the column space of A, along with their dimensions. Justify your answers. 2
2. Let 2 Vi V2 3 0 W2 1 3 2 W3 = 5 -6 Consider the linear transformation f : R3 R3 that satislies f(v1) =W1 f(v2) =W2; f(13) =W3. = (a) 16 points] Let -- 3 2 Use the expression f(cı V1 +cava + c3 V3) = c f(v1) + C2 f(v2) + C3 f(v3) where C1,C2,C3 ER are suitably chosen, to compute f(v).