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.
I like math so i think it's good for me
If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up (+1).
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down (no change).
<span>a) 4.14<u>8</u> ≈ 4.15
b) 5.09<u>2</u> ≈ 5.09
c) 0.45<u>8</u> ≈ 0.46
d) 17.31<u>5</u></span> ≈ 17.32
Answer: 30x= T
Step-by-step explanation:
I solved this by first finding the rate of change (or the amount it changes by each day) which is 30. Then I put the variable (or X) after it which represents the number of days. Then it equals T because that’s the total amount of time spent!
Answer:
yurrrrrrrrrrrrrr
Step-by-step explanation:
