Matrix fun

  • Thread starter Derill03
  • Start date
  • #1
63
0
Any help solving this determinant:

0 1 1 1
1 0 1 1
1 1 0 1
1 1 1 0

My calc says the answer is -3 but there is supposed to be a quicker way than doing all the individual calculations, I did all the calculations and got -3 but there is supposed to be a quicker way. Anyone?
 

Answers and Replies

  • #2
dx
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What way did you use?
 
  • #3
63
0
a11a22a33a44
- a11a22a34a43
+ a11a23a34a42
- a11a23a32a44
+ a11a24a32a43
- a11a24a33a42
- a12a23a34a41
+ a12a23a31a44
- a12a24a31a43
+ a12a24a33a41
- a12a21a33a44
+ a12a21a34a43
+ a13a24a31a42
- a13a24a32a41
+ a13a21a32a44
- a13a21a34a42
+ a13a22a34a41
- a13a22a31a44
- a14a21a32a43
+ a14a21a33a42
- a14a22a33a41
+ a14a22a31a43
- a14a23a31a42
+ a14a23a32a41
 
  • #4
dx
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You can use row and column operations to simplify the determinant. For example,

R2 --> R2 - R3
R3 --> R3 - R4

This makes the first column 0 0 0 1.
 
  • #5
63
0
I get:

0 1 1 1
0 -1 1 0
0 0 -1 1
1 1 1 0

which then a co-factor expansion would give:

0+0+0+0+1*determinant of

1 1 1
-1 1 0
0 -1 1

wheres the -1 come from cause i get an answer of 3? is it supposed to be 0+0+0+0-1?
 
  • #6
dx
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  • #7
56
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Don't forget that the equation for the co-factor expansion includes the term [tex](-1)^{i+j}[/tex] where i is the row and j is the column.

In this case, [tex]i = 4[/tex] and [tex]j = 1[/tex], so this term is [tex](-1)^{4+1} = (-1)^5 = -1[/tex].
 

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