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
- 638 views
- $6.00
Related Questions
- Closest Points on Two Lines: How to use algebra on equations to isolate unknowns?
- How to filter data with the appearance of a Sine wave to 'flattern' the peaks
- Linear independence of functions
- Find $x$ so that $\begin{pmatrix} 1 & 0 & c \\ 0 & a & -b \\ -\frac{1}{a} & x & x^2 \end{pmatrix}$ is invertible
- Certain isometry overfinite ring is product of isometries over each local factor
- Step by step method to solve the following problem: find coordinates of B.
- Linear Algebra Exam
- Find the values of x
