Question

1. The matrices show the enrollment of boys and girls on the basketball, lacrosse, and soccer teams in two towns. (a) If we let matrix A be the matrix for Town A, what is the element , and what does it represent? (b) If we let matrix B be the matrix for Town B, what is the address of the element that represents the number of girls enrolled in basketball in Town B? (c) What is the matrix that results when you subtract matrix A from matrix B? (d) Name the matrix you found in Part (c) matrix C. What is element , and what information does it tell you about the number of girls enrolled in lacrosse in Town B compared with Town A? (e) What is the matrix that shows the enrollment in Town A after a 12.5% increase in enrollment in all sports and in both genders? (Hint: Find 1.125A.)

Answer 1

(a). The element being asked is not specified but elements are named according to the number of the row followed by the number of the column. For example, element a₂₁ is the number of boys enrolled in Lacrosse.

(b). The address is a₁₂.

(c). [196   174]
      [136   169]
      [214    242]

(d). The matrix represents the number of boys and girls from towns A and B enrolled in different sports classes.

(e). 1.125 A = [108   90  ]
                       [72     99  ]
                       [117   135]