Find the volume of the largest open box that can be made from a piece of cardboard 24 inches square by cutting equal squares from the corners and turning up the sides.

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A subspace is a subset that respects the two basic operations of linear algebra: vector addition and scalar multiplication. We say they are “closed under vector addition” and “closed under scalar multiplication”. On a subspace, you can do linear algebra! Indeed, a subspace is an example of a vector space. We see that all of…