a researcher wants to know the typing speed of the students in a large vocational school. the population standard deviation is p
1 answer:
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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.
The complete question is as follows: A Christmas gift is tied with ribbon the bow requires 47cm of ribbon, what is the total length of the ribbon in cm?
Answer: The total length of the ribbon is 177 cm.
Step-by-step explanation:
As there are 4 sides of the rectangular box and 20 cm of ribbon is on each side. This means that a total of = 80 cm is there on the top and bottom.
Hence, length of ribbon attached at the left and right side of the box is as follows.
This means that on both left and right side a total of 50 cm is there.
Therefore, total length of ribbon is as follows.
Total length = 47 cm + 50 cm + 80 cm = 177 cm
Thus, we can conclude that the total length of the ribbon is 177 cm.
