Maths question, matrices

jak731

jak731

jak731

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OK before anyone gets in fast the answer is not 42:p

The question asks for the determinants of matrices A and B, which both come out as 3, it then says explain what you find. I don't have a clue besides saying they just happen to be the same, i know only the bottom row is different so this might have something to do with a decent explanation.

5 -3 3=A
2 -1 1
4 1 2

5 -3 3=B
2 -1 1
6 0 3

Any useful insight appreciated:)

Edit: they looked a bit neater when i made the post, seems the forum just rounds multiple spaces down to one.
 
OK, so if i wanted to i could find the inverse of both matrices, how would this explain why their determinants are the same?
 
Equal determinants means A and B are similar matrices, which means for some X, A=X'BX (that should be -1, but I can't get a superscript). You might also want to note that if in A you add row 2 to row 3 you get B (which is a transformation that doesn't change the determinant).
 
I expect the answer you're expected to give is that the determinants are the same because (as Nimble noted) if you add row 2 to row 3 in A, you get B.
 
You guys are hurting my head.

Why would anyone need to know this stuff in the real world ?

:p
 
Nimble said:
Equal determinants means A and B are similar matrices, which means for some X, A=X'BX (that should be -1, but I can't get a superscript). You might also want to note that if in A you add row 2 to row 3 you get B (which is a transformation that doesn't change the determinant).
Click to expand...

Thanks, i didn't spot that row 3 of B was the second and third row of A added together earlier.

Mr Jack said:
I expect the answer you're expected to give is that the determinants are the same because (as Nimble noted) if you add row 2 to row 3 in A, you get B.
Click to expand...

I still don't see why adding one row to another results in the determinate being the same, is this true for all matrices or only special cases?
 
jak731 said:
I still don't see why adding one row to another results in the determinate being the same, is this true for all matrices or only special cases?
Click to expand...

It's a general result that's true for all square matrices. In fact, you can add any real multiple of one row to another without affecting the determinant.
 
Last edited:
i actually think its true for all matrices isnt it? been a couple years since ive done linear alg which is worrying i suppose..

way i think about it would be to actually think of the matrix representing an equation (for example [3x3].[xyz] ) and think see that adding rows to each other would not change the end result at all - if that makes sense at all..

its an elementary operation - look at RREF/gauss procedure to get easier calcs for dets.
 
spirit said:
i actually think its true for all matrices isnt it? been a couple years since ive done linear alg which is worrying i suppose..

way i think about it would be to actually think of the matrix representing an equation (for example [3x3].[xyz] ) and think see that adding rows to each other would not change the end result at all - if that makes sense at all..

its an elementary operation - look at RREF/gauss procedure to get easier calcs for dets.
Click to expand...

Only square matrices have determinants ;)
 
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