Determine which of the following subsets of R3×3 are subspacesof R3×3 by answering yes or no for each of them.

1. The invertible 3×3 matric

2. The symmetric 3×3 matrices

3. The 3×3 matrices whose entries are allintegers

4. The upper triangular 3×3 matrices

5. The singular 3×3 matrices

6. The 3×3 matrices with trace 0 (the trace ofa matrix is the sum of its diagonal entries)

7. The 3×3 matrices in reduced row-echelonform

8. The 3×3 matrices with all zeros in the firstrow

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1 The invertible 33 matrices Yes The subset of 33 matrices that are invertible is a subspace of R33 because it is closed under addition and scalar mul... View the full answer