Let : R2 → R2 be reflection in the line L in the figure below Find a match from the given choices for each of the follo...
Let T : R2 R2 be projection on the line L in the figure below Find a match from the given choices for each of the following T(u) T(v) T(u)+T(v) T(u+v) T(X) T(O) 4T (u) T(4u) 2T(u)+3T(v) T(2u+3v) True or False? False T(O)-O where O-(0,0) True or False? False for all u and v in R2 T(u+v)=T(u)-T(v) True or False? False T(cu)-T(cu) for all u in R2 and all scalars c True or False? False T is linear Let T...
Given u 0 in Rn, let L-Spanu). For each y in Rh, the reflection of y in L is the point reflyy defined by reflLy 2 projy-y The figure shows that reflyy is the sum of proy andý -y Show that the mapping y- ref y is a linear transformation L = Span{u refly y The refiection of y in a line through the origin Let Ty)- refy2 proy-y. How can it be shown that T(y) is a linear transformation?...
Let u = 2and O - Match each of the following with one of given choices In the choices fields vectors are given in row form such The distance between 2u and -2v is Choose Choose he cross-product uxv is he cross-product vxu is he cross-product uxu is The cross-product vxv is Choose Choose Choose Choose Choose Choose The angle between uxv and u is The angle between uxv and v is Ox(uxv) Choose Choose
linear algebra Let T: R2 R2 be a reflection in the line y = -x. Find the image of each vector. (a) (-3,9) (b) (5, -1) (c) (a,0) (d) (o, b) (e) ( ed) (f) (9)
Problem 3. Let T R2 -R be a linear transformation, with associated standard matrir A. That is [T(TleAl, where E = (e1, ē2) is the standard basis of R2. Suppose B is any basis for R2 a matrix B such that [T()= B{v]B. This matric is called the the B-matrix of T and is denoted by TB, (2) What is the first column of T]s (3) Determine whether the following statements are true or (a) There erists a basis B...
1. Let T: R2 – R? be the map "reflection in the line y = x"—you may assume this T is linear, let Eº be the standard basis of R2 and let B be the basis given by B = a) On the graph below, draw a line (colored if possible) joining each of the points each of the points (-). (). (1) and () woits image to its image under the map T. y = x b) Find the...
Please write carefully! I just need part a and c done. Thank you. Will rate. 3 This problem is to prove the following in the precise fashion described in class: Let O C R2 be open and let f: 0+ R have continuous partial derivatives of order three. If (ro, o) O a local maximum value at (To, Va) (that is, there exist r > 0 such that B. (reo) O and (a) Multivariable Taylor Polynomial: Suppose that f has...
3. Let L be the linear transformation on R2 that reflects each point P across the line y kx (k>0) a) (2 marks) Show that v and v2 - 1 are eigenvectors of L. b) (1 mark) What is the eigenvalue corresponding to each eigenvector? (Hint: No need to calculate the characteristic polynomial or solve a matrix equation. Geometric reasoning should suffice to solve this problem. Drawing a diagram is recommended!) 3. Let L be the linear transformation on R2...
Question 5 For each given vector b and matrix A, determine if b e im(A) 1 -2 3 (a) b 0 A 21 3 0 5 15 (b) b A2-24 9 Question 6 Find the rank and nullity of the given linear transformations T and determine which are one-to-one and which are onto. r+ y ri+r2 Question 7 Find nullity(T) if (a) T:R R2, rank(T) 1 (b) T:RR, rank(T) 0 (c) T : Rs ? R2, rank(T)-1 Question 8 Let...