# Determinant of a 3X3 matrix

M= |3-2x^3_____-4+2x^2+4x^3______0|
|-x^3________1+x^2+2x^3_______0|
|-8-6x^2_____16+12x^2____-1-3x^2|

find the determinant.

* I put the underscores for spacing.

## The Attempt at a Solution

I first tried finding det(A) as if it was a regular matrix of numbers, but that doesn't seem to work. So I'm really not sure how to find the determinant for a matrix of polynomial equations. Where would you actually start?

Astronuc
Staff Emeritus
Well, one can use the fact that the third column has two zeros as entries.

+ - +
- + -
+ - +

I'm not quite getting what I'm supposed to see from the 2 zeros. The way I worked it out before was using the normal determinant method of a11(a22*a33-a32*a23)-a12...etc. Would that not be the correct way to find a determinant for this type of matrix?

M= |3-2x^3_____-4+2x^2+4x^3______0|
|-x^3________1+x^2+2x^3_______0|
|-8-6x^2_____16+12x^2____-1-3x^2|

find the determinant.

* I put the underscores for spacing.

## The Attempt at a Solution

I first tried finding det(A) as if it was a regular matrix of numbers, but that doesn't seem to work. So I'm really not sure how to find the determinant for a matrix of polynomial equations. Where would you actually start?

It should work! If it does not work, check your calculation. It's really the same as the determinant of a matrix of numbers. The fact that there are two zeroes will make the final result not too awful looking. But it's the usual formula for the determinant of a 3 by 3 matrix.

Last edited:
Astronuc
Staff Emeritus