Solving 4x4 Determinant - Find a and b

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Discussion Overview

The discussion revolves around solving for the variables a and b in a 4x4 determinant that is set to zero. Participants explore methods for calculating the determinant, including row operations and the implications of specific values for a and b.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests finding the determinant and setting it equal to zero using row operations.
  • Another participant questions how to rearrange the determinant with row and column swaps, asserting that the determinant is zero regardless of the values of a and b.
  • A different participant challenges the claim that the determinant is zero by providing an example where a = 0 and b = 1, resulting in a non-zero determinant.
  • There is a clarification that the discussion may refer to a rearranged version of the determinant from a deleted post.
  • Participants express confusion about the implications of the determinant being zero and the nature of the set of (a,b) values that satisfy this condition.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the determinant is zero for all values of a and b, as some argue it is while others provide counterexamples suggesting otherwise. The discussion remains unresolved.

Contextual Notes

There are references to deleted posts that may have contained additional context or arguments, which could affect the clarity of the discussion.

cnky
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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?
 
Last edited:
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by finding the determinant and setting it equal to zero. do it by row operations
 
(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)
 
Last edited:
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
 
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.
 
i think hurkyl meant the rearranged one in qutzlcoatl's post, not the original one; i had to think about that too.
 
oh, the deleted one.
 
yes, the now deleted one... at sciencefourms they don't let ordinary users do that for exactly this reason.
 
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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