Answer:
(a)
(b) determinant of the matrix is: -1
(c) number of muffins purchased=18
number of beverages purchased=14.
Step-by-step explanation:
(a) let us assume that the number of muffins purchased=x
number of beverage purchased=y
as a class purchased a total of 32 items that means x+y=32
amount spent=$87.50 that means 3.50x+1.75y=87.50
which could also be written as: 2x+y=50
now in matrix form it could be represented as:
(b) the determinant of the matrix is given by
hence the determinant of the matrix is: -1
(c) now on solving the matrix we need to apply row operations in it to make it a upper triangular matrix so that it would be easy for us to calculate the value of x and y.
we multiply row 1 by 2 and subtract row 2 from it to get
on using the backward substitution in the matrix we get y=14
and x=18
Hence, number of muffins purchased=18
number of beverages purchased=14.