Exam 9: Geometry

Perform the indicated operation. -Let $C = \left[ \begin{array} { r } 1 \\ - 3 \\ 2 \end{array} \right]$ and $D = \left[ \begin{array} { r } - 1 \\ 3 \\ - 2 \end{array} \right]$ . Find $C - 4 D$ .

Find the modulo class to which the number belongs for the given modulo system. -87, mod 9

Solve the problem. -A company makes three chocolate candies: cherry, almond, and raisin. Matrix A gives the amount Of ingredients in one batch. Matrix B gives the costs of ingredients from suppliers J and K. What is The cost of 100 batches from supplier K? $\quad$ $\quad$ $\quad$ $\quad$$\text { sugar choc milk } \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \mathrm{J} \quad\mathrm{K}$ $A = \left[ \begin{array} { l l l } 6 & 8 & 1 \\6 & 4 & 1 \\5 & 7 & 1\end{array} \right] \text { cherry } \text { almond } \quad B = \left[ \begin{array} { l l } 4 & 3 \\4 & 5 \\2 & 2\end{array} \right] \text { suisin moc }$

Decide whether the given set of numbers is a commutative group under the given operation. -Natural numbers; subtraction

Solve the problem. -A company makes three chocolate candies: cherry, almond, and raisin. Matrix A gives the amount Of ingredients in one batch. Matrix B gives the costs of ingredients from suppliers R and S. Multiply the matrices.

Decide whether the given set of numbers is a group under the given operation. -Even integers; addition

Solve the problem. -If Sunday is your starting day, what day will it be 1 year, 43 days from Sunday? (Assume no leap Years.)

Solve the problem. -Does the commutative property of addition, A + B = B + A, hold for matrices A and B? $A = \left[ \begin{array} { r r } - 3 & 1 \\2 & 5\end{array} \right] , B = \left[ \begin{array} { r r } 6 & 2 \\3 & - 2\end{array} \right]$

Provide an appropriate response. -Is there an identity element for the operation of subtraction over the set of integers? Support your claim with an example.

Solve the problem. -A restaurant manager gets a weekend off every 8 weeks. The manager is planning a trip for next Year. If he has already worked 2 weekends in a row following a weekend off, what is the first Week, after 49 weeks from this week, that he will have a weekend off?

Find the product, AB, if possible. - $A = \left[ \begin{array} { r r r } - 2 & - 2 & - 1 \\6 & 5 & - 5 \\4 & - 4 & 4\end{array} \right] , B = \left[ \begin{array} { r r r } - 6 & - 9 & - 5 \\- 6 & 1 & - 6 \\4 & 4 & 3\end{array} \right]$

Solve the problem. -If Wednesday is your starting day, what day will it be 156 days from Wednesday?

Determine the sum or difference in the given clock arithmetic. -5 - 3 (clock 6)

Solve the problem. -If Saturday is your starting day, what day will it be 34 days from Saturday?

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for the given system. -

Solve the problem. -Does the associative property of addition, (A+C), hold for matrices A, B, and C? $\mathrm { A } = \left[ \begin{array} { r r } - 1 & 0 \\4 & 1\end{array} \right] , \mathrm { B } = \left[ \begin{array} { r r } - 1 & 4 \\3 & 1\end{array} \right] , C = \left[ \begin{array} { r r } 1 & 4 \\- 4 & 1\end{array} \right]$

Find the product, AB, if possible. - $A = \left[ \begin{array} { r r r } 1 & 3 & - 2 \\2 & 0 & 4\end{array} \right] , B = \left[ \begin{array} { r r } 3 & 0 \\- 2 & 1 \\0 & 4\end{array} \right]$

Find all replacements (less than the modulus) for the question mark that make the statement true. -9 + ? ≡ 2 (mod 8)

Decide whether the given set of numbers is a commutative group under the given operation. -Whole numbers; multiplication

Perform the indicated operation. -Let $\mathrm { A } = \left[ \begin{array} { r r r } - 8 & 2 & 5 \\ 6 & - 1 & 1 \\ - 4 & 2 & 7 \end{array} \right]$ and $\mathrm { B } = \left[ \begin{array} { r r r } 1 & - 8 & 4 \\ 5 & 3 & 2 \\ - 9 & 1 & 2 \end{array} \right]$ . Find $\mathrm { A } - \mathrm { B }$ .