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pow:problem3f21

Problem 3 (due Monday, October 11)

A student in a linear algebra class looks at her homework problem. It says: Prove that the product $BA$ is the same for any $3\times 2$ matrix $A$ and $2\times 3$ matrix $B$ such that

$AB=\begin{bmatrix} 3 &-1 & 0\\3 &-1 & 0\\-1 & 1 & \end{bmatrix}.$

Unfortunately, the entry in the lower right corner of $AB$ is missing. Find the missing entry and solve the homework problem.

The problem was solved by Ashton Keith, Maxwell T Meyers, and Pluto Wang. Our solution provides a good illustration how to use some basic tools from linear algebra. The submitted solutions are more ad hoc. For details see the following link Solution.