Suppose the 4-vector c gives the coefficients of a cubic polynomial p(x) = c_1 + c_2x+c_3c^2+c_4c

starwolf3wx

starwolf3wx

Answered question

2022-02-22

Suppose the 4-vector c gives the coefficients of a cubic polynomial p(x)=c1+c2x+c3c2+c4c3. Express the conditions
p(1)=p(2),p(1)=p(2)
as a set of linear equations of the form Ac=b. Give the sizes of A and b, as well as their entries.
So far, what I've done was sub in the values and differentiate the polynomials and let it equal to each other after subbing their values.
I get
c1+c2+c3+c4=c1+2c2+4c3+8c4
then,
0=c2+3c3+7c4
as well as
c2+2c3+3c4=c2+4c3+12c4
then,
0=2c3+9c4
What should I do now?

Answer & Explanation

nghycylluzn0

nghycylluzn0

Beginner2022-02-23Added 4 answers

0c1+1c2+3c3+7c4=0
0c1+0c2+2c3+9c4=0
Now write these two equations of four variables in matrix-vector form. You already know that c is 4×1, that is, 4 rows and 1 column. What should the sizes of A and b be?

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