show that d connot be obtained from a norm.

Q: Prove that if a is perpendicular to b, then |a +b|^2 = |a|^2 + |b|^2 .

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Q: 8. The polynomials x - 1, (x - 1)2, and (x - 1)³ span R3[r]. 9. If S and T are finite spanning sets…

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Q: Consider the collection of vectors --000 1 Is Slinearly independent? Carefully explain your answer.

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Q: The column space of A is the set of all vectors that are linear combinations of the columns of A. 3…

A: Given matrix A=24-21-2-57337-86  and  u=3-2-10  and  v=3-13 Remarks If AX=0then x in Null(A)

Q: Suppose v1, V2,..., Vm E V. Prove that {v1, v2, ..., Um} = (span(v1, v2, ..., Um))-.

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Q: Prove that 1 1 16 ≤ (a+b+c+d) = + = + b + ax (²=²+ + + + + + + ² + 1 = 0) d for all positive numbers…

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Q: 25. Show that |v|u + Ju|v and |v|u – |u| v are orthogonal.

A: Two vectors are orthogonal if their dot product is zero. If the dot product of two vectors is zero,…

Q: 1. Show that ||x|| , ||x||||x||₂ are vector norms. 2. Show that if x and y are two vectors, then…

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Q: If p = 2i +j - kand q  = i - 3j +2kdetermine the norm of the addition of p and q, and the magnitude.

A: Consider the given information. p=2i+j-kq=i-3j+2k Find the sum of p and q. p+q=2i+j-k+i-3j+2k=3i-j+k

Q: Suppose that u, v, and w are vectors in an inner product space such that (u, v) 1, (u, w) = :8, (v,…

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Q: onil s 2 S = {v1,V2} = 4 5 7 8. a. Explain why S is linearly independent but is not a basis for R³.…

A: A basis for a subspace S of Rn is a set of vectors in S that is linearly independent and is maximal…

Q: _3. Let x be a convex combination of {y1, . . , yk }. Assume in turn that each y; is a convex…

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Q: 5. a) Let V₁ = H b) Let V₁ = 11 ----- = V3 Does (V1, V2, V3} span R¹? Why or why not? Does (V₁, V2,…

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Q: If some p vectors can span V, then dim V= p True False

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Q: Consider the vectors u1 = (1, 2, 1), u2 = (0, 3, 2) and u3 = (−2, 1, 1). Determine whether the set S…

A: The objective of this question is to determine whether the set of vectors S = {u1, u2, u3} spans the…

Q: 2. 9) is = 1 claim T= {A, B, C } O {[:] [:] [:]} A 13 C Pr 2. b) set C₁ linearly c) In A S = Sa…

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Q: Show that for any arrow, you can pick an axis such that the projection of the arrow on that axis…

A: The statement is true, and to see why, let's consider an arbitrary arrow in three-dimensional space.…

Q: Suppose we have a set of vectors v_1...v_n such that v_1 could be written as a linear combination of…

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Q: Show that Z[V-2] is a Euclidean Domain with respect to the norm N defined by N(a + by-2) = a² + 2b².…

A: This is a problem of abstract algebra.

Q: -1 Let v=-2 then the first norm of v equal 7 -3 Select one: O True False

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Q: Q6) Descrive the sfan ef the given. vecetors algebraically ahd gomebuically. Note that whether ornot…

A: For three linearly independent vectors the span is the entire three dimensional space.

Q: 4.5-1 Verify that ||a|| defines a norm for all n-vectors

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Q: Let A € Rmxn and suppose that the rank of A is m where m is less than or equal to n and be Rm.…

A: Given: We are given a matrix A of size m×n with rank m where m≤n, a vector b of length m×1, and a…

Q: V = {ax² + bx + 3|a, b ≤ R} ≤ P2.

A: Given: V=ax2+bx+3 | a, b∈ℝ⊂ℙ2 To write: The given set as span of minimum number of vectors.

Q: 1.6 (Equality in Cauchy-Schwarz inequality). Prove that |(x, y)| = ||x|| · ||y|| if and only if one…

A: Image is attached with detailed solution.

Q: Find a basis for the null space Nul(A) and a basis for the column space Col(A) of the 2 6 -10 -4 -17…

A: Use basis concept

Q: Verify that lxl:|Ž Ž1% P) is normed spase: and show that nokmed Spase Spase:

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Q: . Let C and D be convex cones in a vector space. Show that Cn D and C+ D are convex cones.

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Q: ovide an illustration of the statement "Every normal space need not be a ular space."

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Q: 7 and bɔ 3 4 Let S be the parallelogram determined by the vectors b, and let A= Compute the area of…

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Q: Find the norm of U = V + 4W -8M V(9.6 , 2.2, -1.6), W(7.2, 4, -3.3) and M(1.1, 3.9, 9.9) Answer:

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Q: Let u4 be a linear combination of {u₁, U₂, U3}. Select the best statement. OA. We only know that…

A: In linear algebra if set A .

Q: Show all the work asap

A: Step 1: Step 2: Step 3: Step 4: