Prove x^4 + a3x^3 + a2x^2 + a1x + a0 is determinant of

[buckaroobill]

This proof was confusing me so any help would be appreciated!

Prove that x^4 + a3x^3 + a2x^2 + a1x + a0 is the determinant of the following matrix:

(When I say a3, a2, a1, a0, that means a sub 3, a sub 2, a sub 1, a sub 0)

In row 1 of the matrix, we have x, -1, 0, 0
In row 2 of the matrix, we have 0, x, -1, 0
In row 3 of the matrix, we have 0, 0, x, -1
In row 4 of the matrix, we have a0, a1, a2, a3+x

 

[tkhunny]

Proof? More like a demonstration. What's keeping you from calculating the determinant? Expansion ny minors? Just give it a try.

 

[pka]

I will get you started!
\(\displaystyle \L \left| {\begin{array}{cccr}
x & { - 1} & 0 & 0 \\
0 & x & { - 1} & 0 \\
0 & 0 & x & { - 1} \\
{a_0 } & {a_1 } & {a_2 } & {a_3 + x} \\
\end{array}} \right| = x\left| {\begin{array}{ccc}
x & { - 1} & 0 \\
0 & x & { - 1} \\
{a_1 } & {a_2 } & {a_3 + x} \\
\end{array}} \right| - a_0 \left| {\begin{array}{ccc}
{ - 1} & 0 & 0 \\
x & { - 1} & 0 \\
0 & x & { - 1} \\
\end{array}} \right|\)

 

[buckaroobill]

Thanks! I figured it out. I think I was confused by all the variables, I organized them in an easier way than I did earlier.