If matirx a is called symmetric if at=a. verify for all 3×3 matirices b+bt is symmetric

Step-by-step explanation:

Given that B is 3x3 matrix.

To prove that B+B^T is symmetry

We know B Transpose matrix will be the matrix got by interchanging the rows and columns of B.

When we interchange rows and columns, we find diagonals remain in the same position

In other words, if i =j

When we add B with B transpose we add diagonal elements twice

and other elements aij with aji for each of the other entry.

Diagonal elements will not pose a problem now when the sum matrix is transposed

B+BT will have ijth entry as =

i.e. the matrix have to be symmetrical

50- 250 is correct i did that one too

step-by-step explanation:

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).