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:
172 cm
Step-by-step explanation:
The total height of the first 7 people is the average of the 7 people multiplied by the number of people, which is 156 * 7 or 1092. Using the same method, the total height of the first 8 people is 158*8 or 1264. The eighth person must be 1264 - 1092 cm tall or 172 cm tall.
Answer: A.
Step-by-step explanation: if you look close enough, you can see exactly how long it is, and see that it does also have the two arrows along with it, but it’s the exact same just tilted a little bit but trust me I believe he correct answer is A.
Answer: 3 3/8
Step-by-step explanation:
subtract 2 3/4 from 6 1/8
Answer:
x=1 I'm not sure if I'm correct
Step-by-step explanation:
4x2x=8x
4x3=12
4x3x=12x
4x2=8
8x+12=12x+8
8x-12x= 8-12
-4x=-4 divide -4x in both side so the answer should be x=1
