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.

Q: Let W be the set of vectors of the form a b A = where a, b, c are real numbers such C that 8b + 3a…

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Q: Linear Algebra

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

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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: closure under adiition is clearly satisfied that is a+b=abalso commutative under addition…

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

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.