Answer:0
Step-by-step explanation:
(0)0.342-0=0.9397(0)
0=0
sin 20= 0.342
cos 20=0.9397
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 