# Determine the determinant

plucker_08
help me guys...

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## Answers and Replies

Staff Emeritus
Gold Member
What have you tried?

Gold Member
MHB
I assume you're familiar with solving a 3x3 Matrix?

Homework Helper
It looks to me like B can be derived from A by "row operations".

(and a few "column" operations- but they work the same way.)

Do you know how row-column operations on a matrix affect its determinant?

Swapping two rows (columns) multiplies the determinant by -1.
Multiplying a row (column) by a number multiplies the determinant by that number.
Adding a multiple of one row (column) to another doesn't change the determinant.

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plucker_08
i've tried the problem...but, the numerical coefficients of b is always wrong...

Homework Helper
Here's my two cents, assuming that I haven't made any arithmetic errors.

Put c=e=g=1, and the rest zero, and compute the determinants for the two matrices. I got |A|=-1, |B|=-12.

Put b=i=1, and the rest zero, and again compute the determinants for the two matrices. I got |A|= -2, |B|= -8.

Consequently, if you're looking for |B| to be a multiple of |A| you are going to be disappointed. So I think that the suggestions given so far for solving this problem will, as the OP says, come up short.

The restriction that |A|=1 is only one equation restricting 7 unknowns. This could get ugly.

Carl

plucker_08
:rofl:

the unknown values of the elements and its determinants are fixed values...

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Homework Helper
plucker_08 said:
the unknown values of the elements and its determinants are fixed values.

Of course everyone knows this already. Perhaps my post was too subtle.

Here's some guesses. You're taking a Linear Algebra class. You still don't have a solution to the problem. The instructor wrote the problem; it wasn't taken from a book. Instead, he made the problem up on his own (and thought that the answer was 12 or 44). Your instructor will admit the error sometime after the homework is due when some of the students complain that they can't work it either.

Carl

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