Match the shapes that have same preimeters
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.
Answer:
0.11 seconds
Step-by-step explanation:
= Time taken by the pebble to hit the water
= Time taken by the sound to travel to the observer
= Time taken by the observer to listen to the splash after stone is thrown = 3 s
a = g = Acceleration due to gravity =
= Speed of sound = 340 m/s
The distance traveled by the pebble
Distance traveled by the sound
The distance traveled by the sound and the pebble is equal
Since the value of
cannot be greater than 3.
So, time taken by the sound to reach the observer is 0.11 seconds.
Time taken by the pebble to hit the water is
Depth of the well is