## Quiz: Excel to Solve Equations

1. How are the number of variables and equations related? Select all that are true.

A. # Variables = # Equations: For linear equations, there is either a unique solution or no solution. For nonlinear equations, there may be multiple or no solution.
Correct. Nonlinear equations may also require a good initial guess to numerically solve.
B. # Variables > # Equations: Additional degrees of freedom. This generally requires an objective function (minimize or maximize a function of the variables) or leads to many potential solutions.
Correct. Optimization is needed when there are more variables than equations to select the best feasible solution that satisfies the constraints.
C. # Variables < # Equations: Additional degrees of freedom. This generally requires an objective function (minimize or maximize a function of the variables) or leads to many potential solutions.
Correct. More equations than variables is generally an overdetermined system where there is no combination of variables that can satisfy all of the equations.

2. The Excel function MMULT allows you to multiply two matrices (i.e. A x B) together with dimensions (n x m) (m x p) where the inner dimensions (m) are the same.

A. True
Correct.
B. A collection of spreadsheet pages
Incorrect.

3. To see the results of the MMULT or MINVERSE function, you must select the result cells, select the input matrices, and then click ALT + ENTER to see the answer.

A. True
Incorrect.
B. False
Correct.