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madhapper
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#1
Report Thread starter 14 years ago
#1
A =
2 1 2
0 3 -1
2 -2 1

find detA using the definition i.e Sum of Sign(sigma)a_1,sigma1....a_n,sig ma(n)


can someone plz explain the formula and tel me how 2 use it
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RichE
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#2
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(Original post by madhapper)
A =
2 1 2
0 3 -1
2 -2 1

find detA using the definition i.e Sum of Sign(sigma)a_1,sigma1....a_n,sig ma(n)


can someone plz explain the formula and tel me how 2 use it
The permutations of three elements 1,2,3 in that order are (with their parities)

1,2,3 even
2,1,3 odd
1,3,2 odd
3,1,2 even
2,3,1 even
3,2,1 odd

And so the determinant formula for a 3x3 matrix is

a11a22a33 - a12a21a33 - a11a23a32 + a13a21a32 +a12a23a11 - a13a22a31

Put your values into that.
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madhapper
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#3
Report Thread starter 14 years ago
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so i get 6-0-4+0+(-2)-12 = -12
correct?
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VCVT17
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I think (A) is a b c
d e f
g h i
det(A) is
a(ei -hf) - b(di -gf) +c(dh -ge)

So the answer is 2(3-2) -1(0+2) +2(0-6) = -12
May it be easier for 3x3 matrix ???
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J.F.N
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(Original post by VCVT17)
I think (A) is a b c
d e f
g h i
det(A) is
a(ei -hf) - b(di -gf) +c(dh -ge)

So the answer is 2(3-2) -1(0+2) +2(0-6) = -12
May it be easier for 3x3 matrix ???
Thats true. There are several ways to do it (Sarrus' rule, expansion by minors, to name a few), but he was looking for a way using the signum definition of determinants.
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