Determine values of some constant which equate linear operators whose linear transformation is through a different basis of the same vector space.
Let $S$ and $T$ be bases for a 2-dim vector space $V$ and let $A$ and $B$ be operators on $V$. Suppose that $[A]_S = \begin{pmatrix} 5 & c \\ c & -1 \end{pmatrix} $ and $[B]_T = \begin{pmatrix} -3 & 0 \\ 0 & 7 \end{pmatrix} $. Determine all values for $c$ such that $A = B$.
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
Blue
184
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 1260 views
- $6.00
Related Questions
- Algebraic and Graphical Modelling Question
- Find a vector parametric form and symmetric form, find minimal distance betwen L and P, consider vectors v and w.
- The Span and Uniqueness of Solutions in a Parametric Matrix
- Consider the plane in R^4 , calculate an orthonormal basis
- Find eigenvalues and eigenvectors of the matrix $\begin{pmatrix} 1 & 6 & 0 \\ 0 & 2 & 1 \\ 0 & 1 & 2 \end{pmatrix} $
- Consider the matrix, calculate a basis of the null space and column space
- Question on Subspaces
- linear algebra
