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MAXImum [283]
2 years ago
11

In the statements below, V is a vector space. Mark each statement true or false. Justily each answer a. The set R is a two-dimen

sional subspace of R3.Choose the correct answer below O A. False, because R2 is not closed under vector addition. O B. True, because R2 is a plane in R3 Ос. False, because the set R2 is not even a subset of R3 OD. True, because every vector in R2 can be represented by a linear combination of vectors inR3 b. The number of variables in the equation Ax 0 equa's the dimension of Nul A. Choose the correct answer below O A. False, because the number of free variables is equal to the dimension of Nul A. O B. True, because the number of variables in the equation Ax 0 equals O C. True, because the dimension of Nul A equals the largest any solution to O D. False, because the number of plvot columns is equal to the dimension of Nud A. c. A vector space the number of columns in A and the number of columns in A equa's the dimension of Nul A. number of Os in any solution to the equation Ax -b, and the equation Ax- 0 always has the trivial solution, so the number of variables is infinite-dimensional if it is spanned by an infinite set Choose the correct answer below O A. True, because the dimension of a vector space is equal to the number of elements in a set that spans O B. Faise, because a basis for the vector space may O C. True, because the dimension of a vector space number of O D. Faise, because all vector spaces are finite-dimensional. d. If dim Van and it S spans V, then S is a basis of V. Choose the correct answer below. the vector space. have only finitely many elements, which would make the vector space finite-dimensional is the number of vectors in a basis for that vector space, and a vector space spanned by an infinite set has a basis with an infinite number of vect O A. False, because the set S must have less than n elements O B. True, because if a vector space is finite-dimensional, then a set that spans t is a basis of the vector space O C. False, in order for S to be a basis, it must also have n elements O D. True, because if a set spans a vector space, regardiess of the dimension of the vector space, then that setis a basis of the vector spaoe e. The only three-dimensional subspace of R3 is R3 itself. Choose the correct answer below Faise, because False, because any subspaces of R3 which contain three-element vectors are three-dimensional, but most of these most three-dimensional subspaces of R3 are spanned by a linearly dependent set of tree vectors, but R can only be sparned by thre Inearly independent vectors subspaces do not contain all of R
D. True, because any three linearly dependent vectors in R3 span all of R3, so there is no three-dmensional subspace of R' that is not R
Mathematics
1 answer:
melomori [17]2 years ago
8 0

Answer:

A. False

B. True

C. False

D. True

Step-by-step explanation:

Only three dimensional subspace for R3 is R3 itself. In a 3 d subspace there are 3 basis vectors which are all linearly independent vectors. Dimension of a vector is number of subspace in that vector. Finite set can generate infinite dimension vector space.

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12 (2 -2)+32 = (x +6) +2
Anestetic [448]

Answer: x = 24

Step-by-step explanation:

Hey there! I will give the following steps, if you have any questions feel free to ask me in the comments below.

<u>Step 1:</u><u> </u><u><em>Remove parentheses.</em></u>

12 (2 − 2) + 32 = x + 6 + 2

<u>Step 2:</u><u> </u><u><em>Simplify 2 − 2 to 0.</em></u>

12 × 0 + 32 = x  + 6 + 2

<u>Step 3:</u><u> </u><u><em>Simplify 12 × 0 to 0.</em></u>

0 + 32 = x +  6 + 2

<u>Step 4:</u><u> </u><u><em>Simplify 0 + 32 to 32.</em></u><em> </em>

32 = x + 6 + 2

<u>Step 5:</u><u> </u>x<u><em> + 6 + 2 to </em></u>x<u><em> + 8.</em></u>

32 = x + 8

<u>Step 6:</u><u> Subtract 8 from both sides.</u>

32 − 8 = x

<u>Step 7:</u><u> Simplify 32 − 8 to 24.</u>

24 = x

<u>Step 8:</u><u> </u><u><em>Switch sides.</em></u>

x = 24

~I hope I helped you! :)~

8 0
3 years ago
Read 2 more answers
a package shaped like a cube has an edge that is 28 cm long. How much space is available to pack inside your box?
Tema [17]
Answer: 21,952 cm³


Explanation:

Volume = 28 x 28 x 28 = 29 152 cm³

7 0
2 years ago
Please help me with this one! Its due today. Thank you ^^
larisa [96]

Step-by-step explanation:

the sum of all angles around a single point on one side of a line is always 180° (a line can always be seen as the diameter of an imaginary circle, so each side corresponds to 180°).

the angles on one side of a line crossed by a second line are mirrored but otherwise exactly the same as on the other side of the line.

a parallel line crossing a third line must have the exact same angles with this third line as the other parallel line. otherwise they would not be parallel. you can say a parallel line mimics the exact same behavior as the other line it is parallel to.

so,

c = 180 - 35 = 145°

a = c = 145°

b = 35°

d = 180 - 110 = 70°

e = d = 70°

f = 110°

g = 180 - 125 = 55°

i = g = 55°

h = 125°

j = 180 - 130 = 50°

m = j = 50°

o = k = d = e = 70° (as this line crosses 2 levels)

l = f = 110°

n = 180 - m - o = 180 - 50 - 70 = 60°

s = 180 - 23 = 157°

p = 23°

r = 68°

q = 180 - p - r = 180 - 23 - 68 = 89°

t = 180 - 68 = 112°

v = w = z = 132° (as this line crosses 2 levels)

A = 180 - 132 = 48°

y = x = u = A = 48°

B = 180 - 39 - 47 = 94°

D = B = 94°

C = 39 + 47 = 86°

E = 47°

F = B + 39 = 94 + 39 = 133°

6 0
2 years ago
HELP I DONT UNDERSTAND :(
AnnyKZ [126]
C
range means all possible y values
3 0
3 years ago
NOT A TEST I REPEAT NOT A TEST ​
Liula [17]

Answer:

I think it's A i hope got it right if i didn't i'm sorry T_T

Step-by-step explanation:

6 0
2 years ago
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