a) The invertible

b) The

c) The

d) The non-invertible

e) The diagonal

f) The symmetric

Inyalan0
2021-12-11
Answered

Which of the subsets of $R}^{3\times 3$ are subspaces of $R}^{3\times 3$ ?

a) The invertible$3\times 3$ matrices

b) The$3\times 3$ matrices whose entries are all integers

c) The$3\times 3$ matrices with all zeros in the third row

d) The non-invertible$3\times 3$ matrices

e) The diagonal$3\times 3$ matrices

f) The symmetric$3\times 3$ matrices

a) The invertible

b) The

c) The

d) The non-invertible

e) The diagonal

f) The symmetric

You can still ask an expert for help

Steve Hirano

Answered 2021-12-12
Author has **34** answers

a) No, cause

encolatgehu

Answered 2021-12-13
Author has **27** answers

If the entries are integers and the linear combination includes $\pi$ as a coefficient, then the entries in the resulting matrix will usually not be integers. Just try it in some simple cases where there are just two terms, with coefficients $\pi$ and 0.

As for (c), a sum of non-invertible matrices is often invertible.

(e) and (f) are subspaces.

It is redundant to say they include 0 if they're closed under linear combinations, because there is a linear combination in which all coefficients are zero.

As for (c), a sum of non-invertible matrices is often invertible.

(e) and (f) are subspaces.

It is redundant to say they include 0 if they're closed under linear combinations, because there is a linear combination in which all coefficients are zero.

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