M lab - a.( X Edufide X G G gmail - X C image X Design X G curvatu X curvatu X M Math - X G math fc x e OA12 ( X Dashbc X C Let L:R X V X eclass.srv.ualberta.ca/mod/quiz/attempt.php?attempt=12777327&cmid=6755852&page=1 *IA : In R', let R be the reflection about the plane which is perpendicular to the vector n = (-4, 4, -4) Find the standard matrix which represents R. R = Check Last saved at 1:00:34 Previous page C W 1:00 AM Mostly clear Q Search 59+ CA ENG US 2023-04-06 3M lab - a.( X Edufide x G gmail - x C image X 3 Design X G curvatu X curvatu X M Math - X G math fc x e OA12 ( X Dashbc X C Let L:R X V X C eclass.srv.ualberta.ca/mod/quiz/attempt.php?attempt=12777327&cmid=6755852&page=3 * IA : (a) Let u and v be (fixed, but unknown) vectors in R". Suppose that T : R" - R" is a linear transformation such that T(u) = 7utv and T(v) = 5u - 3v. on Compute (T . T) (v), where To T is the composition of T with itself. Express your answer as a linear combination of u and v. ( T O T ) ( V) = u + (b) Let v and w be (fixed, but unknown) vectors in R", which are not scalar multiples of each others. Suppose that T : R" - R" is a linear transformation such that T(-2v-3w) =2v+3w and T(v+1w) = -2v+3w. Compute T(v) and express it as a linear combination of v and w. T( v) = + W Check Last saved at 1:00:51 C -30 C ENG 1:00 AM Mostly clear Q Search US 2023-04-06M lab - a.es X Edufide s x @ gmail - G X C image (4 X Design P X G curvature x curvature x M Math - a x G math for x e OA12 (pc X * Course H X. + V X eclass.srv.ualberta.ca/mod/quiz/attempt.php?attempt=12777327&cmid=6755852&page=5 * IA : Problem: Let R : R -> R be the rotation with the following properties. . The axis of rotation is the line L, spanned and oriented by the vector v = (2, -1, -1). . R rotates Ro about L through the angle t = 2 7 according to the Right Hand Rule. Find the matrix which represents R with respect to standard coordinates. on Solution: A right handed ordered ONB B = {a, b, r} for RS, with r the unit vector in the direction of v, has r = b = a = The change-of-basis matrix which converts from 1-coordinates to standard coordinates is OneDrive . . . X [Plet B = Screenshot saved The screenshot was added to your OneDrive. The matrix which represents R with respect to 1-coordinates is -30C Mostly clear Q Search CA W ENG 1:01 AM US 2023-04-06 3M lab - a.es X Edufide S X G gmail - G X C image (4 X Design P X G curvature x * curvature X M Math - a x G math for x @ OA12 (p X * Course H X + V X eclass.srv.ualberta.ca/mod/quiz/attempt.php?attempt=12777327&cmid=6755852&page=5 * IA : b a The change-of-basis matrix which converts from 1-coordinates to standard coordinates is [Ple B The matrix which represents R with respect to B-coordinates is [ R] B+ B = The matrix which represents R with respect to standard coordinates is [R] = C -30C 1:02 AM Mostly clear Q Search ENG US 2023-04-06