Let P2 denote the vector space of all polynomials with degree less than or equal to 2. (a) Show that B = {1 + x + x 2 , 1 + 2x −
x 2 , 1 − 2x − x 2} is a basis for P2. (b) Find the coord
1 answer:
Answer:
The answer is in the the attachment
Step-by-step explanation:
The question you posted was incomplete but i believe below is the complete question;
Let P2 denote the vector space of all polynomials with degree less than or equal to 2. (
a) Show that B = {1 + x + x 2 , 1 + 2x − x 2 , 1 − 2x − x 2} is a basis for P2.
(b) Find the coordinate vector of p(x) = 1 + 2x + 3x 2 relative to the basis B
The answer is explained in the attachments.
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(See the imagine for reference)
Let’s solve where they have a triangle, so the height is 9 cm, the base is 3 cm:
1/2 • 9 • 3 = 13.5
Since there’s 2 triangles we do:
13.5(2) = 27
Now the rectangle in the middle, where the height is 9cm and the base is 12cm:
12 • 9 = 108
Add up the areas:
108 + 27 = 135
Let’s solve where they have a triangle, so the height is 9 cm, the base is 3 cm:
1/2 • 9 • 3 = 13.5
Since there’s 2 triangles we do:
13.5(2) = 27
Now the rectangle in the middle, where the height is 9cm and the base is 12cm:
12 • 9 = 108
Add up the areas:
108 + 27 = 135