Finite Mathematics - Systems of Linear Equations: Matrices

Find the value of when,

$3\times 9\equiv n\ (\text{mod } 4)$ .

Use Cramer's rule to evaluate .

$A= \begin{bmatrix}- \frac{4}{7} & \frac{2}{9} \ \ -\frac{5}{6}& \frac{3}{11} \end{bmatrix}$ and $B= \begin{bmatrix} \frac{5}{7} & \frac{2}{9} \ \ -\frac{5}{6}& -\frac{8}{11} \end{bmatrix}$ .

True or false: , where is the two-by-two identity matrix.

$C = \begin{bmatrix} 1 & 0 & 0 & 0 \ 0 & 2 & 0 & 0 \ 0 &0 &1 & 0 \ 0 & 0 & 0 & 1\end{bmatrix}$

True or false: is an example of a matrix in reduced row-echelon form.

Let $A = \begin{bmatrix} 3 & 1 \ -1 & 2 \end{bmatrix}$ and $B= \begin{bmatrix} 2 & 1 & 3 \ 0 & 1 & 2 \end{bmatrix}$

Find .

$A= \begin{bmatrix} 2 & -6 & -7 \ 3 & 5 & -3 \ 3 & 1 & 9 \end{bmatrix}$ and $B =\begin{bmatrix} -4 & 1 & -9 \ 3 & 6 & -4 \ -2 & 9 & 3 \end{bmatrix}$ ..

True or false:

$A-B = \begin{bmatrix} 6 & -7 & 2 \ 0 & -1 & 1 \ 5 & -8 & 6 \end{bmatrix}$ .

$A = \begin{bmatrix} 2 & 1 & 3 \ - 1 & -2 & -3 \end{bmatrix}$

refers to the two-by-two identity matrix.

Which of the following expressions is equal to ?

is a three-by-four matrix.

Which must be true?

Let $A = \begin{bmatrix} 30 & -10 \end{bmatrix}$ and $B= \begin{bmatrix} 2 & 1 & 3 \ 0 & 1 & 2 \end{bmatrix}$ .

Find .

It is suggested (but not necessary) that you use a calculator with matrix capability to work this problem.

A small factory produces Food A and Food B.

For every pound of Food A produced, one ounce of Food A and two ounces of Food B are consumed. For every pound of Food B produced, one half ounce of Food A and one ounce of Food B are consumed. The factory must meet a monthly demand of two thousand pounds of Food A and three thousand pounds of Food B.

Use a Leontief model to determine how many pounds of Food A and Food B must be produced to meet the demand. Then answer the question - to the nearest whole pound, how many pounds of Food B must be produced?

Systems of Linear Equations: Matrices

Practice Questions