Exam 9: Geometry

Solve the problem. -A traveling salesman sells all over the country in the following pattern: 3 days in New York, 2 Days in Detroit, 1 day in Chicago, 5 days in Los Angeles, 2 days in Houston, 4 days in Washington D.C. and then the cycle starts over. If the salesman is in his 3rd day in Los Angeles, where will he Be 90 days from now?

Find the modulo class to which the number belongs for the given modulo system. --16, mod 9

Solve the problem. -Does the associative property of multiplication, (A × B) × C = A × (B × C), hold for matrices A, B, And C? $\mathrm { A } = \left[ \begin{array} { r r } - 1 & 0 \\3 & 2\end{array} \right] , \mathrm { B } = \left[ \begin{array} { r r } - 1 & 3 \\3 & 1\end{array} \right] , \mathrm { C } = \left[ \begin{array} { r r } 2 & 3 \\- 3 & 1\end{array} \right]$

Determine the sum or difference in the given clock arithmetic. -2 - 6 (clock 6)

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. Multiply The matrices.

Decide whether or not the modulo system forms a group. -{0, 1, 2, 3, 4, 5, 6, 7, 8}; Addition modulo 9

Determine the sum or difference in the given clock arithmetic. -1 + 5 (clock 6)

Decide whether or not the modulo system forms a group. -{0, 1}; multiplication modulo 2

Decide whether or not the modulo system forms a group. -{1, 2, 3, 4, 5}; multiplication modulo 6

Find all replacements (less than the modulus) for the question mark that make the statement true. -7 ∙ ? ≡ 8 (mod 9)

Determine the sum or difference in the given clock arithmetic. -1 - 6 (clock 7)

Solve the problem. -Does the commutative property of multiplication, A × B = B × A, hold for matrices A and B? $\mathrm { A } = \left[ \begin{array} { r r } 3 & 4 \\- 7 & 8\end{array} \right] , \mathrm { B } = \left[ \begin{array} { r r } 1 & - 7 \\4 & 7\end{array} \right]$

Provide an appropriate response. -Does the associative property hold for the set of real numbers under the operation of subtraction? Support your claim with an example.

Provide an appropriate response. -Does the associative property hold for the set of real numbers under the operation of division? Support your claim with an example.

Is the set of integers closed under the operation of division? Support your claim with an example.

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

Perform the indicated operation. - $\left[ \begin{array} { r r } - 4 & 1 \\2 & 5\end{array} \right] + \left[ \begin{array} { l l } 6 & 2 \\1 & 1\end{array} \right]$

Determine the sum or difference in clock 12 arithmetic. -11 - 7

Determine the sum or difference in clock 12 arithmetic. -2 - 9

Find the modulo class to which the number belongs for the given modulo system. --6, mod 16