matrices | Mathematics | Page 1

slim loom Apr 13, 2024, 3:01 PM

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why is the answer not 100?

fierce crystalBOT Apr 13, 2024, 3:01 PM

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slim loom why is the answer not 100?

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buoyant aspen Apr 13, 2024, 3:03 PM

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Do you know the formula?

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A(Adj(A)) = ?

slim loom Apr 13, 2024, 3:04 PM

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|A|^n-1

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n is 2 here

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i was trying to think of matrices like vectors
but it isnt making sense

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like if theres a matrix of a column or a row it can be thought of like a vector

buoyant aspen Apr 13, 2024, 3:10 PM

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slim loom |A|^n-1

It's |A| I?

slim loom Apr 13, 2024, 3:10 PM

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yeah

buoyant aspen Apr 13, 2024, 3:11 PM

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Screenshot_2024-04-13-20-40-58-55_40deb401b9ffe8e1df2f1cc5ba480b12.jpg

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I is:

[1 0]
[0 1]

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So |A| is 10.

slim loom Apr 13, 2024, 3:13 PM

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im just confused
so far ive been thinking of the determinant as a magnitude
like for example if theres a vector <5,5> its magnitude is 5sqrt2 (and the answer stays the same whether i take the scalar 5 out or not) but here when i tried to do that im getting different answers

slim loom Apr 13, 2024, 3:14 PM

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buoyant aspen So |A| is 10.

its not making sense to me T_T

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i meant this

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what am i getting wrong?

buoyant aspen Apr 13, 2024, 3:19 PM

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Why are you making it so difficult?

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It's a direct formula.

slim loom Apr 13, 2024, 3:20 PM

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it feels off to me

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ill have to review the defination maybe. i dont get that

buoyant aspen Apr 13, 2024, 3:22 PM

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slim loom

Let me evaluate it

fervent steeple Apr 13, 2024, 3:23 PM

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adj A is the complex conjugate of the transpose of A, right?

buoyant aspen Apr 13, 2024, 3:24 PM

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fervent steeple adj A is the complex conjugate of the transpose of A, right?

Yea I think.

fervent steeple Apr 13, 2024, 3:30 PM

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@bronze bone would you mind enlightening me?

bronze bone Apr 13, 2024, 3:31 PM

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Its the matrix of cofactors transposed per the definition

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Adjugates aren't adjoints

fervent steeple Apr 13, 2024, 3:32 PM

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Ah that explains it, thanks

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Been a while since I last touched Cramer's rule

slim loom Apr 13, 2024, 3:34 PM

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slim loom what am i getting wrong?

???

fervent steeple Apr 13, 2024, 3:38 PM

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slim loom ???

Your intuition that the determinant as akin to a magnitude is correct to some extent
The determinant is multilinear though, so it gets scaled up every time a column (or each row) is scaled up

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So for a nxn matrix A, |cA| = c^n |A|

slim loom Apr 13, 2024, 3:40 PM

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its hard to visualize

slim loom Apr 13, 2024, 3:41 PM

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fervent steeple So for a nxn matrix A, |cA| = c^n |A|

I'll keep this in mind

quaint vector Apr 13, 2024, 5:09 PM

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slim loom I'll keep this in mind

You should try to prove this , it will make you easy to remember

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You can prove this by using properties of determinants

#matrices