Determine whether the statement below is true or false. Justify the answer. A subspace of R" is any set H such that (i) the zero vector is in H, (ii) u, v, and u + v are in H, and (iii) c is a scalar and cu is in H. Choose the correct answer below. O A. The statement is false. Conditions (ii) and (iii) must be satisfied for each u and v in H, which is not specified in the given statement. B. The statement is false. It must also be separately specified that u - v are in H when u and v are in H. O C. The statement is true. Any set of elements of R" that satisfies conditions (1). (i), and (i) is a subspace by definition. D. The statement is false. It must also be separately specified that au + bv are in H when u and v are in H and a and b are scalars. O E. The statement is false. The zero vector does not need to be in a set for the set to be a subspace.

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A: A non empty subset W of a vector space V is said to be a subspace of V is:1. for all u, v ∈W we…

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A:

Q: Let V be the set of all positive real numbers. Determine whether V is a vector space with the…

A: V=x∈R+ which is set of positive real numbers addition operation x+y=xy scalar multiplication cx=xc

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A:

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Q: Linear Algebra

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Q: Find a basis for the subspace of P2 spanned by the given vectors.  1 + x, x2, -2 + 2x2, -3x

A: Basis are (1, 1,0), (0, 0,1), (-2, 0,2), (0, -3, 0)

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A: We determine whether S is a vector space with the given operations.

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A:

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A: W=span

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Q: If a subspace of V of R contains the standard vectors ei, e2, eg, then V must be R. True False

A: We will show that V is a subset of R³. Then, we can claim that, V = R³

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A:

Q: your work. 91² - r°, t+ 21°, 1 +t- 9r?

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Q: Determine whether U is a subspace of R³. U = {(2r, –s²,t)lr,s, and t E R}

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A: we will first find the equivalent matrix and then reduce it to row echelon form

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Q: Determine if S=R (real numbers) where -1 is not included, is a vector space with the operations:…

A: S does not form vector space.

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A: We want to find standard basis of P5.

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.