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melisa1 [442]
3 years ago
14

Explain how to determine if something is a vector space or not

Mathematics
1 answer:
nlexa [21]3 years ago
6 0
All you do is referring to the following definition:

Definition: A<span> vector space </span>is a set V on which two operations + and · are defined, called<span> vector addition </span>and<span> scalar multiplication.</span>

The operation + (vector addition) must satisfy the following conditions:

Closure: If u and v are any vectors in V, then the sum   u + v   belongs to V.

(1)<span> Commutative law: </span>For all vectors u and v in V,     u + v = v + u

(2)<span> Associative law: </span>For all vectors u, v, w in V,     u <span>+ (v</span> + w<span>) = (u</span> + v) + w

(3)<span> Additive identity: </span>The set V contains an<span> additive identity </span>element, denoted by 0, such that for any vector v in V,     0 + v = v   and   v + 0 = v.

(4)<span> Additive inverses: </span>For each vector v in V, the equations     v + x = 0   and   x + v = 0     have a solution x in V, called an<span> additive inverse </span>of v, and denoted by - v.

The operation · (scalar multiplication) is defined between real numbers (or scalars) and vectors, and must satisfy the following conditions:

Closure: If v in any vector in V, and c is any real number, then the product   c · v   belongs to V.

(5)<span> Distributive law: </span>For all real numbers c and all vectors u, v in V,     c · <span>(u</span> + v) = c · u + c · v

(6)<span> Distributive law</span>: For all real numbers c, d and all vectors v in V,     (c+d) · v = c · v + d · v

(7)<span> Associative law</span>: For all real numbers c,d and all vectors v in V,     c · (d · v) = (cd) · v

(8)<span> Unitary law</span>: For all vectors v in V,     1 · v = <span>v</span>

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Can somebody plz help answer all these questions correctly!! (Only if u know or remember how to do this) lol thanks!!!
kvasek [131]

Answer:

17. 42

18. 12

19. 12

20. 12

Step-by-step explanation:

Simply substitute the given values into the variables. So if m = 6 and n = 2:

7m = 7(6) = 42

6n = 6(2) = 12

mn = (6)(2) = 12

3m - 6 = 3(6) - 6 = 18 - 6 = 12

6 0
3 years ago
Read 2 more answers
Combine like terms.<br> (7+x)(7-x)
aleksandrvk [35]

Answer:

x^2-49

Step-by-step explanation:

when u multiply the numbers in parenthesis u get 49-7x+7x-x^2 and when u simplify that u get x^2-49

8 0
3 years ago
A catapult launches a boulder with an upward velocity of 120 ft/s. The height of the boulder, h,
Vlad1618 [11]

Answer:

Reaches a maximum height of 235.00 feet in 3.75 seconds.

Step-by-step explanation:

The height of the boulder, h,  in feet after t seconds is given by the function is given by :

h=-16t^2+120t+10 .....(1)

For maximum height, put \dfrac{dh}{dt}=0

i.e.

\dfrac{d(-16t^2+120t+10)}{dt}=0\\\\-32t+120=0\\\\32t=120\\\\t=3.75\ s

Put t = 3.75 in equation (1). So,

h=-16(3.75)^2+120(3.75)+10\\\\h=235\ \text{feet}

So, the boulder's maximum height is 235 feets and it takes 3.75 s to reach to its maximum height.

3 0
3 years ago
In the line 3y=4x-1 and 9y=x+3 are parallel to each other the value of q is
jonny [76]
Do you mean the value of y? there is no q in these equations.
5 0
2 years ago
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How do I find the absolute value
pychu [463]

Absolute value of function = - 9 / 3 .

The absolute value or modulus of a real number x, denoted by |x|, is the non-negative value of x without regard to its sign. Namely, |x|=x if x is a positive number, and |x|=-x if x is negative (in which case negating x makes -x positive) , and |0|=0.

For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3. The absolute value of a number may be thought of as its distance from zero.

x ≥ 1.52 / 3 x - 1 = 2 / 3 x + 4⇒ -1 = 4 which is not possible .Now for all x ≤ 1.5- 2 /3 x + 1 = 2 / 3 x + 4⇒ 4 / 3 x = -3  x = - 9 /4 Hence absolute value = - 9 / 3 .

To learn more on absolute value follow link :

brainly.com/question/13041863

#SPJ9

8 0
1 year ago
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