Answer:
a) 3√11
b) C: (3x - 1)(x - 1) = (3)C1 + (1 + x)C2 + (3 - 3x + 3x²)C3
c) C = {3i, 2j, 3k} or C = {3i, 4/3j, 5/3k}
Step-by-step explanation:
a) C = {3, 1 + x, 3 - 3x + 3x²)
For x ≤ 2, C = {3, 3, 9)
P2, the vector space, C = {3i, 3j, 9k)
∴ P2 = √3² + 3³ + 9² = √99 = 3√11
b) - 3 + 12x - 9x² = 0
(3x - 1)(x - 1) = 0
x = 1 or 1/3
C: (3x - 1)(x - 1) = (3)C1 + (1 + x)C2 + (3 - 3x + 3x²)C3
c) -3 + 12x - 9x² ⇒ C = {3, 1 + x, 3 - 3x + 3x²)
From -3 + 12x - 9x²= 0
(3x - 1)(x - 1) = 0
x = 1/3 or x = 1
For x= 1
Cordinate vector, C = {3i, 2j, 3k}
For x= 1/3
Cordinate vector, C = {3i, 4/3j, 5/3k}