linear algebra

[granite wagon]

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[quick forge]

is this very simple

where for the first det its -27 and for the second -18

or do column operations differ from row ops

[chilly star]

determinant is invariant under transpose

so doesnt matter

but yes, just invoke multilinearity of the determinant

[quick forge]

so for the first question it will be -27

how can i get the second one

[chilly star]

It's clear 5,8,11 is an arithmetic sequence given by 3n+2 for n=1,2,3

So the matrix is [u|3(1,2,3)+2(1,1,1)|v]

Invoking multilinearity in the 2nd column gives 3(-4)+2(-3)

[quick forge]

so the determinant will result in the product of that

-18

[chilly star]

Yes, -12-6=-18...