## 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.