# 4x4 determinant

#### cnky

4x4 determinant(from my exam)

a+b-- a--- a--- a
a--- a+b-- a--- a
a---- a-- a+b-- a detA=0
a---- a--- a--- a+b

How do I find a and b?

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#### matt grime

Homework Helper
by finding the determinant and setting it equal to zero. do it by row operations

#### Hurkyl

Staff Emeritus
Gold Member
(note: this is a response to a deleted reply)

How do you rearrange it like that with row and column swaps? (P.S. the determinant of the matrix you created is clearly zero, no matter what a and b are)

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#### quetzalcoatl9

Hurkyl said:
How do you rearrange it like that with row and column swaps? (P.S. the determinant of the matrix you created is clearly zero, no matter what a and b are)
yes you are right

#### mathwonk

Homework Helper
hurkyl, you have me puzzled as to why the determinant is clearly zero. take b = 1, a = 0 for instance. then the determinant sure looks like 1 to me, since the matrix is then the identity.

therefore the set of (a,b) with det = 0 apparently forms a curve in the complex (a,b) plane.

#### matt grime

Homework Helper
i think hurkyl meant the rearranged one in qutzlcoatl's post, not the original one; i had to think about that too.

#### mathwonk

Homework Helper
oh, the deleted one.

#### matt grime

Homework Helper
yes, the now deleted one... at sciencefourms they don't let ordinary users do that for exactly this reason.

#### quetzalcoatl9

matt grime said:
yes, the now deleted one... at sciencefourms they don't let ordinary users do that for exactly this reason.
sorry about that, i didn't want to leave something that was wrong and further confuse the matter. i leave it up next time.

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