Determine whether ?: ?^2 → ?^2, ?(?, ?) = (? + ?, ? − ?) is a linear transformation

Please describe using text keyboard (NOT HANDWRITING), what is meant by “The Kernel,” and “The Range” of a linear transformation. Put simply, what are they?

Solve the problem. 2 3 1 Let A = S -7 5 Define a transformation T: R³ 24-49 10 30 -28 12 O O O 18 42 O 29 -15 < Previous and u = 2 by T(x) = Ax. Find T(u), the image of u under the transformation T

<+C 0 docr googie.com/Torme/d/e/1FAlpOLSeW2TFYeCSaPcrm-RyfIMbcUo2FBZ68X29uEEaXn829hw/viewfom/hr.submssi 3) Identify a sequence of transformations that will transform figure J into figure K. What is the first transformation?" O (x y) - (y, x) Oa) - (x, y) O)(x y 1) O (x. y)- (x y 1)

Which ordered pair is NOT in the inverse of the relation given by xy² - 3x = 12? O (0,-4) O (4,1) O (3,2) O (2,12) O (1,-6)

3. Determine if the following mappings are linear transformations. Explain your answer. (а) Т: Р.(R) — Р.(R), where T (ао + ајx) — (Зао — 4а,) + ај + аga? (b) Т: Р: (R) P.(R), where T(ао +ајz + az2?) 3 (аэ — 12а1) + (ај + Зао) 2

Find the inverse relation of R = {(a, 5), (b, 3), (c, 2), (d, 1)}.

(x,y) → (x+5,y) Describe the transformation in words

True or False: The relation R = {(-2, 0), (0, 2), (0, -2), (2, 0)} is a function.

The vertices of a square are H(0, 2), I(2, 0), J(0, –2), and K(-2,0). Which statements are true of the image of HIJK after the given composition of transformations? Select all that apply. Step 1: (x, y) → (-y, x) Step 2: (x, у) — (Зх, Зу) H" (-2,0) HIJKE H'I'J'K' H'TJ'K'~ H"I"J"K" J" (6, 0) Y = xis a line of symmetry for the HIJK and H"I"J"K"