Consider the 3 × 3 matrix a =   0 1 k 2 k −6 2 7 4  . for what values of k is matrix a invertible? (a) k ∈ r (b) all real k except 2 and 5 (c) k ≥ 0 (d) k = 0 (e) no value of k makes a invertible

All real k except 2 and 5.

Step-by-step explanation:

For a matrix to be invertible the determinant of it should not be equal to zero.

A matrix P is invertible if |P| ≠ 0

The matrix given here is:

For the above matrix to be invertible:

Matrix is invertible for all real k except 2 and 5.

dont trust me im no expert these losers made me fail a test bro this sucks

step-by-step explanation:

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.