(a) A: R3 (b) A: Rs[z] R3[x], A: (a, b, c) ax + bx² + cx³. R2×2, A: pp(1) p(2) p(3) p(4) (c) A: R2 R2, A: (a,b) (a+b, 0). T → (d) A: R3 R₂[x], A: (a, b, c) 2a + bx + cx². (e) A: R3 R3, A: (a, b, c) (ab, b-c, a-c).
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Which of the listed mappings is an isomorphism of
![(a) A: R3
(b) A: Rs[z]
R3[x], A: (a, b, c) ax + bx² + cx³.
R2×2, A: pp(1) p(2)
p(3) p(4)
(c) A: R2
R2, A: (a,b) (a+b, 0).
T →
(d) A: R3
R₂[x], A: (a, b, c)
2a + bx + cx².
(e) A: R3
R3, A: (a, b, c) (ab, b-c, a-c).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F758ad870-c64b-4610-bdc2-72ab1ebe40bf%2F3f71e4d2-899f-4635-8570-77dab6b938d6%2Fnjrz3a_processed.png&w=3840&q=75)
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- 2 – Find: (a) 3a ,(b) a + b, (c) a-b, (d) la + b|, (e) a- b|, (f) 3a – 4b and (g) | 5a + 2b|. If 1. a = 2i + 4j, b = -i+ 4j 2 a = (1, 1), b = (2, 3) 3 a = (4,0), b (0,-5) 4 a= i-dj, b = }i+ j 5. a = -3i + 2j, b= 7j 6 a = (1, 3), b = - Sa 7. a = -b, b = 2i – 9j 8. a = (7, 10), b = (1,2) %3D %3D %3! %3D %3DFind (a) u ∙ v, (b) v ∙ v, (c) ||u||2, (d) (u ∙ v)v, and (e) u ∙ (5v).u = (3, 4), v = (2, −3)|Vx (x + 2) dx = (A) x기2+3 (B) + + (C) ( + 2x) + C (D) V++c 3/241/2 4 5 1 + C