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## Homework Statement

Prove

det [a+p b+r c+s; d e f; g h i] = det [ a b c; d e f; g h i] + det [p r s; d e f; g h i]

## Homework Equations

none

## The Attempt at a Solution

i'm not sure how to prove this though its seems obviously true =S

- Thread starter Jennifer1990
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- #1

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Prove

det [a+p b+r c+s; d e f; g h i] = det [ a b c; d e f; g h i] + det [p r s; d e f; g h i]

none

i'm not sure how to prove this though its seems obviously true =S

- #2

tiny-tim

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General tip: if you can't see how to prove something, always go back to the

Sooo … what is the definition of the determinant?

- #3

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A determinant is a function depending on n that associates a scalar, det(A), to an n×n square matrix A.

I dont see how this helps me tho.. I'm sorry T_T

- #4

Mark44

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That's a very general description of what a determinant is, but not a definition. Do you know how to calculate the determinant of a 3 x 3 matrix?

I dont see how this helps me tho.. I'm sorry T_T

- #5

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To calculate the determinant of a 3x3 matrix, u take the sum of the cofactors multiplied by the number in each entry of the original matrix . which is then also multiplied by (-1)^n, where n represents the position of the entry

- #6

Mark44

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Not quite. As you have written it, it appears that you are saying you have a sum of 9 terms for a 3 x 3 matrix, which is not true.

You can evaluate a 3 x 3 matrix by cofactors going across any row or down any column. So for your first matrix, one way of evaluating the determinant is to expand across the top row, resulting in (a + p)A

Now, have at it...

- #7

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um actually, thats wat i meant o.o

- #8

Mark44

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But that's not what you said, so it seemed to me that you didn't really understand how to calculate the determinant.

- #9

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ohh sorry.

so, um, are u asking me to apply that formula to the determinants in the question and show that the determinants are the same?

- #10

Mark44

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Yes, of course.

- #11

tiny-tim

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(just got up :zzz:)

me too!

- #12

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Is there another way to prove this question other than finding the determinant for the matrices?

- #13

tiny-tim

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but the question isIs there another way to prove this question other than finding the determinant for the matrices?

so,

get on with it!

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