Determine whether the subset of Mn,n is a subspace of Mn,n with the standard operations of matrix addition and scalar multiplica
tion. The set of all n x n invertible matrices a. subspace b. not a subspace
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Please find the attached file for a better understanding of the solution provided here:
ABCD is the swimming pool and PQRS is the extent of the swimming pool plus the concrete walkway which is 6 yards wide.
Now, we know that the length is 8 yards shorter than twice it's width. Thus,
l=2w-8
Now the area of the region, A'B'QP will be: length x width. Now, the length here is l+6+6=2w-8+12=2w+4 and width is 6.
Thus, area of the region A'B'QP is (2w+4)x6=12w+24
Likewise, the area of the region D'C'RS will similarly be 12w+24 too.
Now, the area of the region BB'C'C will be 6 x w=6w
Similarly, the area of the region AA'D'D will be 6 x w=6w
Therefore, the total area of the walk way will be:
Therefore, length, l will be:
Therefore, the dimensions of the swimming pool are:
Length, l= 21 yards and Width, w=14.5 yards
