Judy has 2 3/4 bags of rock that she wants to use in her yard. Each bad will cover 310.2 sq ft. How many square feet will Judy be able to cover if she used all the bags of rocks? Round up your answer to the neatest tenth place.

853.1 sq ft

Step-by-step explanation:

Total bags of rock = 2 3/4

Each bag will cover 310.2 sq ft

How many square feet will Judy be able to cover if she used all the bags of rocks?

Total Square feet covered = number of bags of rock × area covered by each bag

= 2 3/4 × 310.2 sq ft

= 11/4 × 310.2 sq ft

= 853.05 sq ft

To the nearest tenth

= 853.1 sq ft

You can proceed as follows:

Step-by-step explanation:

Suppose that the matrix is invertible, and suppose that at least one of the matrices is not invertible. Without loss of generality suppose that the matrix is not invertible.  Remember the important result that a matrix is invertible if and only if its determinant is nonzero. Then,

On the other hand, the determinant of a products of matrices is the product of the determinants of the matrices, that is to say,

But we supposed that is not invertible. Then . Then . This contradicts the fact that

and then the three matrices must be invertible matrices.