Which of the subsets of R3×3 are subspaces of R3×3? a) The invertible 3×3 matrices b) The 3×3 matrices whose entries are all integers c) The 3×3 matrices with all zeros in the third row d) The non-invertible 3×3 matrices e) The diagonal 3×3 matrices f) The symmetric 3×3 matrices

Question

Which of the subsets of R3×3 are subspaces of R3×3?  a) The invertible 3×3 matrices  b) The 3×3 matrices whose entries are all integers  c) The 3×3 matrices with all zeros in the third row  d) The non-invertible 3×3 matrices  e) The diagonal 3×3 matrices  f) The symmetric 3×3 matrices

Steve Hirano · Accepted Answer

a) No, cause

encolatgehu · Accepted Answer

If the entries are integers and the linear combination includes π 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 π 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&#039;re closed under linear combinations, because there is a linear combination in which all coefficients are zero.

Which of the subsets of PSKR^{3×3}ZSK are subspaces of PSKR^{3×3}ZSK? NSK a)

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