# 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 be viewed only if**

- The questioner was satisfied and accepted the answer, or
- The answer was disputed, but the judge evaluated it as 100% correct.

Blue

157

The answer is accepted.

Join Matchmaticians Affiliate Marketing
Program to earn up to 50% commission on every question your affiliated users ask or answer.

- answered
- 156 views
- $6.00

### Related Questions

- Show that eigenvectors of a symmetric matrix are orthogonal
- Let $H$ be the subset of all 3x3 matrices that satisfy $A^T$ = $-A$. Carefully prove that $H$ is a subspace of $M_{3x3} $ . Then find a basis for $H$.
- Find the values of x
- Linear Algebra - Vectors and Linear Systems
- Find the null space of the matrix $\begin{pmatrix} 1 & 2 & -1 \\ 3 & -3 & 1 \end{pmatrix}$
- Step by step method to solve the following problem: find coordinates of B.
- [Linear Algebra] $T$-invariant subspace
- Character of 2-dimensional irreducible representation of $S_4$