Question

I haven't done linear algebra in ages, so I have this determinant question...

Answer 1

ill healp

Answer 2

ok whats the promble,

Answer 3

I vaguely remember this,

Answer 4

The differential equation is y'''+y'=tant

Answer 5

But I can't remember why we have that (-1) there

Answer 6

And what does that power represent, row?

Answer 7

the -1 has to do with an occuring phenomemon of taking a cofactor matrix i believe

Answer 8

Oh right this is a theorem rings a bell cofactor expansion or something

Answer 9

spose we 'move' rows and columns about while taking determinants

a b
c d

det= ad - bc

but spose we swap it as

b a
d c the determiant has been altered by a sign change

Answer 10

when we take cofactor expansions, we are essentially pulling a row/col to the 11 position, and taking its sub determinant .. at least thats what i recall

the -1 is an adjustment for that

Answer 11

Ah gotcha, that's why we can have 0 0 1 in the middle row third row etc we're essentially factoring out the row or column and then have the -1 so it stays the same kind of haha, I probably butchered that, but I think I get it now

Answer 12

:) its a work in progress but yeah

Answer 13

Ok cool, thanks!