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
167
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
- 392 views
- $6.00
Related Questions
- Calculate the inverse of a triangular matrix
- Frontal solver by Bruce Irons? Am I using the right Algorithm here?
- Space of all matrices with given column space
- Find eigenvalues and eigenvectors of $\begin{pmatrix} -3 & 0 & 2 \\ 1 &-1 &0\\ -2 & -1& 0 \end{pmatrix} $
- [Linear Algebra] Diagonalizable operator and Spectrum
- Singular Value Decomposition Example
- two short Linear Algebra questions
- Numerical Linear Algebra Question