91Ó°ÊÓ

If you are performing a breakeven analysis for a business and their cost and revenue equations are dependent, explain what this means for the company's profit margins.

Can you explain why a partial fraction decomposition is unique? (Hint: Think about it as a system of equations.)

Examining Cramer's Rule, explain why there is no unique solution to the system when the determinant of your matrix is 0 . For simplicity, use a \(2 \times 2\) matrix.

Can we multiply any column matrix by any row matrix? Explain why or why not.

Explain what it means in terms of an inverse for a matrix to have a 0 determinant.

Can you explain whether a \(2 \times 2\) matrix with an entire row of zeros can have an inverse?

Is there only one correct method of using row operations on a matrix? Try to explain two different row operations possible to solve the auqmented matrix $$ \left[\begin{array}{rr|r} 9 & 3 & 0 \\ 1 & -2 & 6 \end{array}\right] $$

When you graph a system of inequalities, will there always be a feasible region? If so, explain why. If not, give an example of a graph of inequalities that does not have a feasible region. Why does it not have a feasible region?

The determinant of \(2 \times 2\) matrix \(A\) is \(3 .\) If you switch the rows and multiply the first row by 6 and the second row by 2 , explain how to find the determinant and provide the answer.

Can a matrix with an entire column of zeros have an inverse? Explain why or why not.