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MAXImum [283]
3 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]3 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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Answer:

(Answer D)

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The value of the function f(g) after simplifying and putting 2 in place of <em>x</em> is -20 and the value of f(g(2)) is 418.

<h3>What is composite function?</h3>

When a function is written inside the another function, then such function is called the composite function.

The first function given in the problem is,

f(x) = x^2 - x - 2

The second function given,

g(x) = - 6x - 8

To find out the value of g(2), put the 2 on place of variable x in the above equation as,

g(2) = - 6(2) - 8\\g(2)=-12-8\\g(2)=-20

The composite function f(g(x)) can be given as,

f(g(2))= (-20)^2 - (-20) - 2\\f(g(2))=418

Thus, the value of the function f(g) after simplifying and putting 2 in place of <em>x</em> is -20 and the value of f(g(2)) is 418.

Learn more about the composite function here:

brainly.com/question/10687170

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