Question

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 2021-01-17

\((A|B) = tr(B^tA)\).

Let U be the subspace of V consisting of the symmetric matrices. Find an orthogonal basis for \(U^\perp\) where \(U^{\perp}\left\{A \in V |(A|B)=0 \forall B \in U \right\}\)

asked 2020-11-30

\(M=\begin{bmatrix}a & b \\c & d \end{bmatrix}\)

and define \(M^{\#}=\begin{bmatrix}d & b \\c & a \end{bmatrix}\) Characterize the matrices M such that \(M^{\#}=M^{-1}\)

asked 2021-06-26

Determine if the statement is true or false, and justify your answer. (a) Different sequence s of row operations can lead to different reduced echelon forms for the same matrix. (b) If a linear system has four equations and seven variables, then it must have infinitely many solutions.