1
answer
0
watching
132
views
10 Nov 2019
questions 16,18,20
Bookmarks Window Help ???U.8· 17 d21.pdx.edu (no subject)-saad7@???.edu-Portland State U 4 Ch each vector x in R2. 16. Let T: RR be a linear transformation that maps utol and maps v3 into Use the fact that T is linear to find the images under T of 3u, 2v, and 3u + 2v 17. Lete,-?,e,-H'y?=EI,andy2=[61], and let T : R2 ? R2 be a linear transformation that maps e1 into y, and maps e2 into y2 Find the images of and 22 . Hint: Express both I 3 and zas a linear combination of ei and e2. Then use the fact that T is a linear transformation! 18. An afine transformation T : Rn ? Rm has the form T(x)-Ax+ b, with A ar mon matrix and b in Rm. Show that T is not a linear transformation when b?0. (FYI: Affine transformations are important in computer graphics!) 19. Let T:RRm be a linear transformation, and let (vi, v2, v3) be a linearly dependent set of vectors in Rn. Explain why the set (T vi),T(v2),T(vs)) is linearly dependent. (Hint: First, write the linear dependent relation among vi, V2, V3, then apply T to both sides of this linear dependent relation!) 20. Note that in this exercise column vectors are written as rows, so x(2). Define a function T by T(x1,T2) = (22 i-3 r2M, 5x2). What is the domain of T? Codomain? Define a matrix A such that T(x)-Ax. ? | 2 |12 ?
questions 16,18,20
Bookmarks Window Help ???U.8· 17 d21.pdx.edu (no subject)-saad7@???.edu-Portland State U 4 Ch each vector x in R2. 16. Let T: RR be a linear transformation that maps utol and maps v3 into Use the fact that T is linear to find the images under T of 3u, 2v, and 3u + 2v 17. Lete,-?,e,-H'y?=EI,andy2=[61], and let T : R2 ? R2 be a linear transformation that maps e1 into y, and maps e2 into y2 Find the images of and 22 . Hint: Express both I 3 and zas a linear combination of ei and e2. Then use the fact that T is a linear transformation! 18. An afine transformation T : Rn ? Rm has the form T(x)-Ax+ b, with A ar mon matrix and b in Rm. Show that T is not a linear transformation when b?0. (FYI: Affine transformations are important in computer graphics!) 19. Let T:RRm be a linear transformation, and let (vi, v2, v3) be a linearly dependent set of vectors in Rn. Explain why the set (T vi),T(v2),T(vs)) is linearly dependent. (Hint: First, write the linear dependent relation among vi, V2, V3, then apply T to both sides of this linear dependent relation!) 20. Note that in this exercise column vectors are written as rows, so x(2). Define a function T by T(x1,T2) = (22 i-3 r2M, 5x2). What is the domain of T? Codomain? Define a matrix A such that T(x)-Ax. ? | 2 |12 ?
Hubert KochLv2
13 Apr 2019