For any $$ matrix $$ and any vector $$, $$ is the matrix obtained from $$ be replacing column $$ by $$.

Given that $$ and $$ compute the following.

$$

$$

Use Cramer’s rule to determine the unique solution $$ to the equation:

$$
$$ (reduce the fraction)

Use Cramer’s rule to determine the unique solution $$ to the equation:

$$ (reduce the fraction)
$$ (reduce the fraction)

For which of the following matrices can you use cramer’s rule to find the solution to $$ for some vector $$ of the appropriate dimension?
$$
$$
$$ }vspace5pt

For which of the following matrices can you use cramer’s rule to find the solution to $$ for some vector $$ of the appropriate dimension?
$$
$$

Theorem: Let $$ be an invertible $$ matrix. Then

Let $$. Compute the following.

$$

$$

$$