Homework Help: Matrix determinant polynomial

1. Jul 27, 2006

Bob

Evaluate the following determinant. Write your answer as a polynomial in x.

$$\begin{array}{|lcr|}a-x&b&c\\1&-x&0\\0&1&-x\end{array}$$

2. Jul 28, 2006

durt

Just find the determinant as usual. A cofactor expansion from one of the rows or columns containing a zero is probably the easiest way.

3. Jul 28, 2006

HallsofIvy

You do realize, don't you, that you are expected to show us what you have tried so we can suggest changes? What durt suggested is very general but without knowing where you are having trouble we can't be more specific. It won't help you for someone else to do it for you.

(I confess that I find the answer amusing!)

4. Jul 28, 2006

Data

clever problem :rofl:

5. Jul 28, 2006

Bob

The answer is $$-x^3+ax^2+(b-a)x-a+c$$

6. Jul 28, 2006

Data

not quite

7. Jul 28, 2006

interested_learner

Show us the work!!!! How did you get that wrong answer?

8. Jul 29, 2006

Bob

$$-x^3+ax^2+bx+c$$

9. Jul 30, 2006

HallsofIvy

What part of "Show us the work!!!! How did you get that wrong answer?" did you not understand?

10. Jul 30, 2006

Bob

I am sorry.

$$(a-x)(x*x-1)-1(-bx-c)+0\\=ax^2-a-x^3+x+bx+c\\=-x^3+ax^2-(a-b)x-a+c$$

11. Jul 30, 2006

d_leet

Recheck your first term, (a-x)(x*x-1) isn't quite right.

12. Jul 31, 2006

HallsofIvy

Okay, you are expanding by the first column:
$$(a-x)\left|\begin{array}{cc}-x & 0 \\1 & -x\end{array}\right|- (1)\left|\begin{array}{cc}b & c \\ 1 & -x\end{array}\right|$$
As dleet said, check that first number. 0*1 is not 1!