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:
bbbbbbbbbbbbbbbbbbbbbbb
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
49 ≥ 10d
49 ≥ 10(8)
49 ≥ 80
49 has to be greater than or equal to 80
d = 8 isn’t a solution
Answer:
Gustavo
Step-by-step explanation:
if anything this looks like 38-19n, if the first term is n=1.
But as that isn't an option, gustavo should be correct, as his sequence would go down by 19 each time (yuki's would go up by 19 each time, not down like the sequence shows)
