Multiply 240 by 5 to get 1200 miles then add the 40 from the first day so it took 5 days
The area formula for a rectangle = Length x Width
Let length = L and width = W.
We also know that the length is 3 yards longer than twice it's width.
SO this means L = 3 PLUS 2 times W
L = 3 + 2W
Now plug that into the area formula and we get:
Area = (3 + 2W) x W
You'll need to multiply everything in the brackets by W.
So what would (3 + 2W)x W = ?
Length of the original ribbon = 2/3 yard
Length of the ribbon in which the actual ribbon has to be cut = 1/12 yards
The above information's are already given in the question. It is required to find the number of pieces that the ribbon can be cut with the length that is already mentioned.
Then
Number of pieces that will be there = (2/3)/(1/12)
= (2 * 12)/3
= 24/3
= 8
So the actual ribbon can be cut into 8 pieces and each piece will have a length of 1/12 yards. Hopefully the procedure for doing this problem is clear to you. this is the easiest method for attempting these kind of problems.
6.5 is the mean of the data
A vector space 
is a subspace of a vector space 
if
- is non-empty,
- for any two vectors
we have 
, and - for any scalar
and 
we have 
.
It's easy to show the first condition is met by all the sets in parts (a-g).
(a) is a subspace of 
because adding any 2x2 diagonal matrices together, or multiplying one by some scalar, gives another diagonal matrix.
(b) and (c) are also subspaces for the same reasons.
(d) is not a subspace because because this set of matrices does not contain the zero matrix.
(e), however, is a subspace. Any linear combination of matrices in this set always yields a matrix with 0 in row 1, column 1 entry.
(f) is a subspace. A symmetric matrix is one of the form
Adding two symmetric matrices gives another symmetric matrix:
(g) is not a subspace. Consider the matrices
Both matrices have determinant 0, but their sum is the identity matrix with determinant 1.
