1. The linear span of a set S is the(a) largest subspace contained in S.(c) smallest subspace contained in S.2. The subspace-08>(a) x - 2y-z = 0(b) largest subspace containing S.(d) smallest subspace containing S.in R is a plane whose equation is(b) 2r-y-z-0(c) z-y-2z=0(d) r-y-z=0

To show that linear span of a set is the (a) largest subspace contained in S. (b) largest subspace…

Answered: 1. The linear span of a set S is the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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4. Which of the following subsets of R³ constitute a subspace of R³? [Here, x = (₁, §2, §3).] (a) All x with §₁ = ₂ and §3 = 0. (b) All x with ₁ = - ₂ + 1. (c) All x with positive 1, 2, §3. (d) All x with ≤₁ − ₂ + 3 = k = const.
4. your answer. 3 Determine whether each of the following sets is a subspace of R³ and justify (a) W = {(x1, x2, x3) € R³ : x1 + x3 = 2x2, x1 x3 = 3x₂}. - (b) W = {(x1, x2, x3) € R³ : x3 + 1 = x1 +eª2}. (c) W = {(x₁, x2, x3) € R³ : x² + x² = 0}.
choose the correct letter
4.
2. Determine whether the given set is a subspace of the given space. If it is a subspace give a proof, if it is not give a counterexample. (a) V = R¹, S = (b) W = {[1]. a ER -b+c=0. V = R³. ab (c) W = (ar²+2x+e: a,care real numbers) V = P₂ (d) W = The set of all symmetric matrices (A= A). V= M₂x2(R).
Let (Z,t) be a cofinite topological space. The set {.-74,-72,-70,70,72,74,..} is
-(1)-(). and v= Describe the set Span {u, v, 3u, 2u - 5v, 0} geometrically, where u = 0
9. S= {(6,2,1), (-1,3, 2)} is: a. a linearly independent set of R b. a linearly dependent set of R.
Let H = span -23] 17 -11 -22 Find the dimension of H. -2 11 8 -5 -10 -4 3 -2
In each case determine whether subset W is a subspace of R³. Assume that a, b, c are real numbers. Support your answer. (a) W = {(a,b,c)|a - 2b =0} (c) W = {(a, 2a, c+a)} (b) W = {(a, b, c)|a²2b² = 0} (d) W = {(a, b, 0)|ab=0}
Prove using partitions that Explain this result geometrically. cb+c f* f (x)dx = ft+ f(x − c)dx. - a a+c
If R = {(1, 2), (1, 4), (2, 3). (3, 1), (4, 2)}, what is the symmetric closure of R? O {(1, 2), (2, 1), (1, 4), (4, 1), (2, 3), (3, 2), (3, 1), (1, 3), (4, 2), (2, 4)} O {(1, 1), (1, 2), (1, 4), (2, 2), (2, 3), (3, 1). (3, 3), (4, 2), (4, 4)} O {(1, 2), (1, 4), (2, 3), (3, 1), (4, 2)} O {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1). (3, 2). (3, 3), (3, 4), (4. 1), (4, 2), (4, 3), (4, 4)}

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1. The linear span of a set S is the (a) largest subspace contained in S. (c) smallest subspace contained in S. 6) G (b) largest subspace containing S. (d) smallest subspace containing S.