Alex, Bart, and Carl are brothers. Alex is the oldest and Carl is the youngest. The sum of the ages of the three brothers is 42. Alex's age is 3 more than twice Carl's age. The difference between Bart's and Carl's age is 7 years. Which system of equations could be used to determine the ages of all three brothers?

A = Alex

B = Bart

C = Carl

B - C = 7

A + B + C = 42

C / 2 x 3 = A

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints

solution:

→c= a b , that is product of a and b is possible only when when a is m × n matrix and b is n × p matrix.

that is, number of columns of a= number of rows of b.

so, size of matrix , c= a b is , if a = (m × n)matrix

b= (n × p)matrix

then a b = [ (m × n)matrix] ×[   (n × p)matrix ]

→→c= a b= [m × p ] matrix

→→size of product a b will be equal to = number of rows of a × number of columns of b