Matrix determinant

Bob

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

[tex]\begin{array}{|lcr|}a-x&b&c\\1&-x&0\\0&1&-x\end{array}[/tex]


Please help me! thanks.

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.

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!)

Data

clever problem

Bob

The answer is [tex]-x^3+ax^2+(b-a)x-a+c[/tex]

Data

not quite

interested_learner

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

Bob

[tex]-x^3+ax^2+bx+c[/tex]

HallsofIvy

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

Bob

I am sorry.


[tex](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[/tex]

d_leet

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

HallsofIvy

Okay, you are expanding by the first column:
[tex](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|[/tex]
As dleet said, check that first number. 0*1 is not 1!