- #1

- 63

- 0

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?

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- Thread starter Derill03
- Start date

- #1

- 63

- 0

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?

- #2

dx

Homework Helper

Gold Member

- 2,112

- 41

What way did you use?

- #3

- 63

- 0

- 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

Homework Helper

Gold Member

- 2,112

- 41

R2 --> R2 - R3

R3 --> R3 - R4

This makes the first column 0 0 0 1.

- #5

- 63

- 0

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

Homework Helper

Gold Member

- 2,112

- 41

is it supposed to be 0+0+0+0-1?

Yes.

- #7

- 56

- 0

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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