If you manipulated a matrix so all the entries above the diagonal entries are 0s, how would the solution differ from when made the entries below the diagonal entries 0s?

(Exact Answer) When all the entries above the diagonal entries are 0, the solution will not be different from when all the entries below the diagonal entries are 0. This is because in both cases, there will be one row that would be left with just one unknown element, thus giving us the solution to the other unknowns through back-substitution. For instance, in a linear system with three unknowns, x, y, and z, the traditional triangulated form will give us the value of z first; however, if the entries above the diagonal entries in the matrix are 0, then we will get the value of x first. In either case, the solution will be the same.

Step-by-step explanation:

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

step-by-step explanation: