Linear Algebra

From: "jennifer" <scrilla_12_1999@xxxxxxxxx>
Date: 12 Oct 2006 12:02:51 -0700

Let V denote a 10-dimensional vector space, and let U and W denote the
subspaces of V, where dim U= 8 and dim W= 9.
Prove that there are only two possible values of the dimension of UnW.

Proof;-

Using the dimension formula:

Dim V = Dim U +Dim W - Dim (UnW)

Dim V>= Dim U +Dim W - Dim (UnW)

i.e. 10>= 8 +9- Dim (UnW)

10>= 17- Dim(UnW)

-7 >= -Dim(UnW)

Dim(UnW)>= 7

i.e. Dim(UnW)>7 and Dim(UnW) = 7

are these the two possible answers?

.

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