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The derivative of a+bx+cx2 is b+2cx+0x 2 . (a) Write the 3 by 3 matrix D such that D a b

Chapter 5, Problem 5.6.13

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QUESTION:

The derivative of a+bx+cx2 is b+2cx+0x 2 . (a) Write the 3 by 3 matrix D such that D a b c = b 2c 0 . (b) Compute D 3 and interpret the results in terms of derivatives. (c) What are the eigenvalues and eigenvectors of D?

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QUESTION:

The derivative of a+bx+cx2 is b+2cx+0x 2 . (a) Write the 3 by 3 matrix D such that D a b c = b 2c 0 . (b) Compute D 3 and interpret the results in terms of derivatives. (c) What are the eigenvalues and eigenvectors of D?

ANSWER:

Step 1 of 3

Given the derivative of expression is

(a) The  by  matrix  such that

Since, the first element of the column is , then  and all the other element should be .

The second element of the column is , then  and all the other element should be .

The third element of the column is , then and all the other element should be.

Therefore, the matrix form as;

        

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