Find the determinant of a matrix

[sara_87]

Bonsoir everyone

can anyone confirm if i got the answer right or wrong:

Question:

find the determinant of A. A is a matrix and is equal to

1 5 -3
3 -3 3
2 13 -7

(i think you've already guessed that i don't have latex)

My answer:

i got -18


I would be grateful if anyone could confirm my answer, and if it's wrong i'll write out all the steps that i did in order to get that answer

Merci

 

[Mindscrape]

Did you use ninja math or cofactors? I like ninja math:

[(1*-3*-7)+(5*3*2)+(3*13*-3)]-[(-3*-3*2)+(3*13*1)+(5*3*7)]=? <----- Is that -18?

 

[SunGod87]

You're correct.

 

[turdferguson]

According to my TI-83, that's it

 

[sara_87]

Thank you all so much!...(i knew i was right ;) )

and you could help me further by telling me how to find det(B^3) where det B= 4

i don't think that it's as simple as 4^3...is it?

 

[sara_87]

ninja math?

 

[matt grime]

Det is multiplicative (Det(XY)=Det(X)Det(Y)). You have been taught this. So use it.

 

[sara_87]

so it is 4^3, and my answer is 64

 

[Mindscrape]

Ninja math, basketweave, whatever you want to call it. You slice along the diagonals. So if you have matrix A, you would do

(A11*A22*A33+A12*A23*A31+A21*A32*A13)-(A13*A22*A31+A12*A21*A33+A23*A32*A11)

 

[radou]

Ninja math, basketweave, whatever you want to call it. You slice along the diagonals. So if you have matrix A, you would do

(A11*A22*A33+A12*A23*A31+A21*A32*A13)-(A13*A22*A31+A12*A21*A33+A23*A32*A11)

That 'Ninja math' method is also called the Sarus rule, and it only applies for determinants of matrices of order 3.

 

[Mindscrape]

Yes I forgot to mention it is only for 3x3. Sarus rule? I did not know that. I prefer ninja math other Sarus rule though.