Do the matrices have inverses? justify your answer.
a. −2 6
−3 9
b. −2 6
3 9

a. No

b. Yes

Step-by-step explanation:

as we know the inverse of the matrix is A⁻¹ = (adjA)/det(A)

If the determinant of the matrix is 0 then the inverse of that matrix does not exists.

For first matrix the determinant is

|A| =

Hence the inverse of this matrix does not exists.

|B| =

Since the determinant of the matrix in the second option is non-zero .Hence it's inverse exists.

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).