True/False: Let $$ be a linear transformation. The matrix for $$ relative to the bases $$ and $$ for $$ and $$ respectively is given by: where $$.
True False
True/False: Let $$ be a linear transformation. Let $$ and $$ be bases for $$ and $$ respectively. Let $$ be the matrix for $$ relative to $$ and $$. Then which of the following equations is true?
$$ $$

Let$$ and $$ be bases for the vector spaces $$ and $$ respectively. Let $$ be a linear transformation. Given the equations below, find the matrix for $$ relative to $$ and $$.

$$

Let $$ and $$ be bases for the vector spaces $$ and $$ respectively. Let $$ be a linear transformation. Given the equations below, find the matrix for $$ relative to $$ and $$.

$$

Let $$ be a basis for some vector space $$. If the linear transformation $$ sends vectors written with respect to the basis $$ to vectors written with respect to the basis $$, then the matrix for $$ relative to $$ (or the $$-matrix for $$) satisfies:
True False

True/False. Suppose $$ where $$ is a diagonal $$ matrix. If $$ is the basis for $$ formed fromt he columns of $$, then $$ is the $$-matrix for the transformation $$.
True False
See the diagonal matrix representation theorem on page 291 of Lay.

Suppose $$ where $$ are given below. Let the linear transformation $$ be defined by $$. Which of the following gives a basis $$ for $$ with the property that $$ is diagonal.

$$ $$ $$
See the diagonal matrix representation theorem on page 291 of Lay.