12.42
12°+.42(60)
12°25.2'
12°25'+.2(60)
12°25'12"
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Answer:
Amphitrite1040
Step-by-step explanation:
The answer is y = 35x + 20.
In order to find this, start with two ordered pairs. For the purpose of this problem, we'll use (1, 55) and (2, 90). Now we use the slope formula to find the value next to x in the equation.
m(slope) = (y2 - y1)/(x2-x1)
In this equation (x1, y1) is the first ordered pair and (x2, y2) is the second. Plug in to the equation and solve.
m = (90 - 55)/(2 - 1)
m = 35/1
m = 35
Now that we have the slope, plug that into the equation along with either point to find the intercept (the last number).
y = mx + b
55 = 35(1) + b
55 = 35 + b
20 = b
Now that we have the slope and intercept, we can use each to fill in those blanks.
y = 35x + 20
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.