# Find the value of the determinant

• Dec 28th 2009, 09:20 PM
zorro
Find the value of the determinant
Question : Find the value of the determinant

$\displaystyle D= \begin{vmatrix} x+a & b & c \\ a & x+b & c \\ a & b & x+c \end{vmatrix}$ Compute $\displaystyle \frac{dD}{dx} |_{x=1}$

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Solution:
(My work)

$\displaystyle |D| = x^3 + ax^2 + bx^2 + cx^2 = x^3 + x^2(a+b+c)$

$\displaystyle \frac{dD}{dx} |_{x=1}$..............I am stuck here i dont know what to do here
• Dec 28th 2009, 10:35 PM
mr fantastic
Quote:

Originally Posted by zorro
Question : Find the value of the determinant

$\displaystyle D= \begin{vmatrix} x+a & b & c \\ a & x+b & c \\ a & b & x+c \end{vmatrix}$ Compute $\displaystyle \frac{dD}{dx} |_{x=1}$

---------------------------------------------------------------
Solution:
(My work)

$\displaystyle |D| = x^3 + ax^2 + bx^2 + cx^2 = x^3 + x^2(a+b+c)$

$\displaystyle \frac{dD}{dx} |_{x=1}$..............I am stuck here i dont know what to do here

You will be happy to know that your expression for the determinant is correct. Now differentiate it with respect to x. Then substitute x = 1 into the derivative.
• Dec 29th 2009, 12:10 AM
zorro
(Clapping)(Dance)I did it correctly .........yippy .........and mr fantastic praised me (Bigsmile)