Tell which of the following subsets are subspaces of the vector space of nxn mat

Jaden Easton 2021-10-13 Answered
Tell which of the following subsets are subspaces of the vector space of nxn matrices, \(\displaystyle{M}_{{{n}{x}{n}}}\)
a) The set of nxn matrices with a zero determinant.
b) The invertible matrices.
c) The diagonal matrices.
d) Upper triangular matrices.
e) The nxn matrices, all of \(\displaystyle{M}_{{{n}{x}{n}}}\).

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Jayden-James Duffy
Answered 2021-10-14 Author has 26785 answers
Subspace of the vector space of nxn matrices, \(\displaystyle{M}_{{{n}{x}{n}}}\) are the subsets of the diagonal matrices and upper triangular matrices.
Not exactly what you’re looking for?
Ask My Question
0
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-12-11
Which of the subsets of \(\displaystyle{R}^{{{3}×{3}}}\) are subspaces of \(\displaystyle{R}^{{{3}×{3}}}\)?
a) The invertible \(\displaystyle{3}\times{3}\) matrices
b) The \(\displaystyle{3}\times{3}\) matrices whose entries are all integers
c) The \(\displaystyle{3}\times{3}\) matrices with all zeros in the third row
d) The non-invertible \(\displaystyle{3}\times{3}\) matrices
e) The diagonal \(\displaystyle{3}\times{3}\) matrices
f) The symmetric \(\displaystyle{3}\times{3}\) matrices
asked 2022-01-04
(a) Suppose U and W are subspaces of a vector space V. Prove that \(\displaystyle{U}\cap{W}={\left\lbrace{v}:{v}\in{U}\text{and}\ {v}\in{W}\right\rbrace}\) is a subspace of V.
(b) Give an example of two subspaces U and W and a vector space V such that \(\displaystyle{U}\cup{W}={\left\lbrace{v}:{v}\in{U}\text{or}\ {v}\in{W}\right\rbrace}\) is not a subspace of V.
asked 2021-12-08
Tell, please, what are the \(\displaystyle\prec\) and \(\displaystyle\succ\) operators for when you use it with matrices?
asked 2021-11-28
Find a basis for the space of \(\displaystyle{2}\times{2}\) lower triangular matrices
Basis =
asked 2021-05-14
Determine whether each of the given sets is a real linear space, if addition and multiplication by real scalars are defined in the usual way. For those that are not, tell which axioms fail to hold. The function are real-valued. All rational functions f/g, with the degree off ≤≤ the degree ofg (including f = 0).
asked 2021-11-08
Find the value(s) of h for which the vectors are linearly dependent. Justify each answer.
\[\begin{bmatrix}1 \\5 \\-3\end{bmatrix},\begin{bmatrix}-2 \\-9 \\6\end{bmatrix},\begin{bmatrix}3 \\h \\-9\end{bmatrix}\]
asked 2021-11-09
Describe all solutions of Ax=0 in parametric vector form, where A is row equivalent to the given matrix.
\[\begin{bmatrix}1 & 3 & 0 & -4\\2 & 6 & 0 & -8\end{bmatrix}\]
...