Non-invertible?

Algebra Level 3

What is the least number of elements that need to be 0 in order for some 3 × 3 3\times 3 matrix to be non-invertible?

3 2 0 1

Daniel Liu by Daniel Liu , 21, USA

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2 solutions

A matrix A A is non-invertible iff det ⁡ ( A ) = 0 \det(A) = 0 . As an obvious counter-example, consider a matrix with all ones. □ \square

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Daniel Liu
Jun 9, 2014

Sorry, I was bored.

The last number is obviously 0. Supplying an example is an exercise to the reader.

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The question doesn't seem to be phrased very properly. I took it to mean, what is the least number of zeroes so that ANY 3x3 matrix with that number of zeroes is non-invertible. You seem to mean, what is the least number of zeroes so that SOME 3x3 matrix with that number of zeroes is non-invertible. In the first case, the answer should be 7 (I think), and it is less trivial.

Michael Tang - 7 years ago

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I agree with Michael's interpretation.

Calvin Lin Staff - 7 years ago

Sorry. It was like 10:30 PM or something, I wasn't really thinking clearly.

Daniel Liu - 7 years ago

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