(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine if the set of all singular 2 x 2 matrices are a subspace of [itex]R^{2}[/itex]

2. Relevant equations

If a, b, c, and d are the entries of a 2 x 2 matrix, then their determinant, [itex] ad - bc = 0[/itex] if the matrix is singular.

3. The attempt at a solution

I have been doing other problems like this without much trouble by taking two general form objects in the set and checking the closure relations for addition and scalar multiplication. However, I'm not sure how I can represent thegeneral formof a singular 2 x 2 matrix so that I can perform addition and scalar multiplication on it.

For example, the matrix [itex]X[/itex] with [itex] x_{11}=a, x_{22}=b, x_{21}=a,[/itex] and [itex] x_{22}=b[/itex] is an example of a singular 2x2 matrix but it isn't a general form, which I'd need to determine if the set of singular 2x2 matrices are a subspace.

If I took two matrices like x and checked the closure relations I believe I'd find they are satisfied, which my books tells me is the wrong answer.

Thanks.

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# Homework Help: Determining a Subspace

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