- #1

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Could anyone give me a proof for the following theorem?

Theorem : Ax=0 has a non-trivial solution iff det(A)=0

Thanks in advance.

/Sunny

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- Thread starter sunny110
- Start date

- #1

- 11

- 0

Could anyone give me a proof for the following theorem?

Theorem : Ax=0 has a non-trivial solution iff det(A)=0

Thanks in advance.

/Sunny

- #2

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- #3

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A matrix [itex]A[/itex] represents a linear transformation in a given basis. The determinant is a property of the matrix, but it's

Now we can see what a zero determinant means: it means the transformed volume element is zero. This transformation has squished it down into a lower-dimensional subspace, which means the

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