Let M be a subset of R2 and M = { (1,2), (1,1) } Find Span (M) (1)

Q: (a) Let M = R. Give the radius r and the center c of B(-2,5) n B(6, 7). ne

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: Let v1 =[1,4,-2] , v2 =[-2,-3,7] , b =[4,1,h] FIND all value(s) h such that b is in span{v1 , v2 }

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Q: Find the transitive closure of R={(0,1),(0,2),(1,1), (1,3),(2,2),(3,0)}

A: Given relation is                              R=(0, 1), (0, 2), (1, 1), (1, 3), (2, 2), (3, 0) we…

Q: Is the set W={ f(x)e P(F): f(x)=0 or f(x) has degree n } a subspace of P(F) if n21? Justify your…

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Q: Prove that the set of mxn upper triangular matrices is a subspace of Mmxn(F).

A: We have to prove that -

Q: Show the span {(1,0, 1), (-1, 2, 3), (0, 1, – 1)} is all of R'.

A: Let x=1, 0, 1, y=-1, 2, 3 and z=0, 1, -1. We have to show that spanx, y, z is actually the vector…

Q: find the value of a for which       [ 4 ] v = [ a ]       [-4]       [ 3 ] is in the set…

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Q: Q4) Determine whether the set S is linearly independent or linearly dependent a) S = {(2,1,–2),…

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Q: The symbol L(S) represents the linear span for any nonempty subset S of a Vectorspace V Select a…

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Q: Show that R³ is spanned by S = {(1,1,1), (1, –1, 0), (0, 1, – 1)}.

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Q: Set f(a,b) = (1+ a + b) + (2 + 2a + b)x + (1 + a + 26)r² and F = {f(a, b) : a,b e R} a subset of…

A: Given that fa,b=1+a+b+2+2a+bx+1+a+2bx2 and F=fa,b : a,b∈ℝ is a subset of ℝ2x. The objective is to…

Q: Let T (V₁, V2, V3) w = (4, 1, −1). = (2v1 + V2, 2v2 − 3v₁, V₁ — V3). Find T(–4,5,1) and pre-image of

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Q: Suppose y1 ( x), y2 ( x), y3 ( x) are three different functions of x. The vector space they span…

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Q: Show that  ℝ2 = span([1 1], [1 -1])

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Q: Let 2 3 X = X2 = X3 = 6. 3 4 4 (a) Show that x1, X2, and x3 are linearly dependent. (b) Show that x¡…

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Q: 22. Let v₁ = (1, 6, 4), v₂ = (2, 4, -1), V3 = (-1, 2, 5), and W₁ = (1, -2,-5), w₂= (0, 8, 9). Use…

A: Given vectors are Here observed that So we have each of .In other words ,

Q: Find Imf and Kerf of the following linear maps: a) f(x₁, x₂ + x3) = (x₁ - x₂ + 2x₂) x₁ + x3, x₁ + x₂…

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Q: Let X₁ = [1 3 −1 1]²‚×₂ = [3 −1 3 1]′, and x3 = [-1 2 −3 1]. Is b = T an element of span{X₁, X₂,…

A: No, we can write it.

Q: X b) Let T 10 Find the Kernel of T. Write down the range of T as a span of independent 5x vectors.…

A: Obtain Kernel of T as follows.

Q: Prove Span ({ 1, 1+2, 1+ x + x² })= P₂ (R).

A: We have to show Span1,1+x,1+x+x2=P2ℝ

Q: Show that (5,0,3) is in the span of S= {(1,1,0), (1,0,1), (1,1,1)}.

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Q: (2) Let aj = (1,2, -1), a2 = (3,0, 1) and bị = (-1, 10, 7), b2 = (1, 2, 0) in R³. %3D (a) Is a, in…

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Q: Give an example of (v1, V2, V3) and (W1, w2, W3) independent se- span(wi, w2, w3) and {v1, v2, v3}(…

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