- #1
charlies1902
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The problem is attached. The problem is "find a basis for the range of the linear transformation T."
p(x) are polynomials of at most degree 3. R(T)={p''+p'+p(0) of atmost degree 2}
This is pretty much as far as I got. I'm not sure how to do the rest.
I'm thinking of picking a random function, let's say:
ax^3+bx^2+cx+d
p'(x)=3ax^2+2bx+c
p''(x)=6ax+2b
p"+p'+p(0)=(6ax+2b)+(3ax^2+2bx+c)+(d)
The book says the answer is {1, x, x^2}. Is it because in the line above, you can see that x^2, x are in there and 1 is there in the form of d?
p(x) are polynomials of at most degree 3. R(T)={p''+p'+p(0) of atmost degree 2}
This is pretty much as far as I got. I'm not sure how to do the rest.
I'm thinking of picking a random function, let's say:
ax^3+bx^2+cx+d
p'(x)=3ax^2+2bx+c
p''(x)=6ax+2b
p"+p'+p(0)=(6ax+2b)+(3ax^2+2bx+c)+(d)
The book says the answer is {1, x, x^2}. Is it because in the line above, you can see that x^2, x are in there and 1 is there in the form of d?