Denote the column vectors of the matrix 11,922.. , ann +] True, false, or uncertain: a; is orthogonal to a; for all i j? "Prove" your answer by "showing" the essential steps/arguments. [ts] Under what conditions is diag{a₁₁, 22, ..., ann} = ₁(diag{a₁₁, 22, ..., ann})? "Prove" your answer by "showing" the essential steps/arguments. ..Under what conditions is diag{a₁1, a22, ..., ann} (diag{b1₁₁,b22, ..., bnn})' = In? "Prove" your answer by "showing" the essential steps/arguments

Q: Show whether or not the set of vectors B = {U, V, W} where U = V = and W = 0 is a basis for R³.

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Q: Given three non-zero vectors, a, b & C, is it possible to evaluate a b Explain with an example. •6•²

A: We have given three non-zero vector.

Q: Let X = TONT. 1 and 3 0 A = 0 3 1 0 -2 -4 -4 0 3 00 -2 0 0 -4 0 1 -1 01 1 0 0

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Q: Let a = (2,3,6) and b = (3,4,2) be vectors.  Compute the cross product aXb

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Q: Let m = (-3,1,5) and n = (5,-1,2). calculate the vector p = n - ((m*n)/(m*m))*m.

A: here we get p=0

Q: Suppose we know that Write A 6 as a linear combination of the vectors 5 8- 5 6 = 0 H + 6 1 1 -DE-B H…

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Q: Using the vector r=[0.5 + e-(=/3), €-(2/6), 2], determine the difference between the transpose()…

A: % the value of pi pi=22/7 ; % define given vector rr=[0.5+e^(-j*pi/3) ,e^(-j*pi/6),2 ];fprintf('The…

Q: Determine whether the given vectors (1, 1,-1, 1), (1,-1, 2,-1), (3, 1, 0, 1) in R* are lincarly…

A: Given vectors are: (1, 1, -1, 1) , (1, -1, 2, -1) , (3, 1, 0, 1) We have to determine whether the…

Q: 5.) Let V₁ = - -2 V₂: Is b a linear combination X₁V₁ + x₂ V₂ = b. 5 b=4 of v₁ and v2; that is, does…

A: Here we have to check whether the given vector b→=745 is linear combination of vectors v1→=1-2-5 and…

Q: Write v as the sum of two vectors, one in Span fu,} and one in Span fu2,u3,u4}. Assume that fu1 .u4}…

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Q: Represent the product [a* · (b* × c)][m* · (n* × p*)] as a sum of such terms, which contain scalar…

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Q: Find the length of the projection of 3   onto the vector -3…

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Q: (i) Prove that { (1, 2, 1) , (2, 1, 5) , (1, –4, 7) } is linear dependent subset of R³. (ii)…

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Q: Are the vectors = [−5_3 −1], v = [02-1] and w = [-25 21 -8] linearly independent? Choose If they are…

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Q: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

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Q: -3 -3 9. 2 Let A = -3 -6 12 and b = 3 -3 -2 13 -5 Denote the columns of A by a1, a2, a3, and let W =…

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Q: Represent the vector ⟨16,8,−14⟩ in terms of the ordered basis B={⟨5,−2,−2⟩,⟨1,−4,2⟩,⟨−1,−5,3⟩}.

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Q: Let Q "Ax – x'b – C be such that A is positive definite. | Which of the following statements is…

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Q: Express the vector x as a linear combination of the u's. --0-0-0- 0, U₂5, U3 = -50 Select one: O A.…

A: Two matrices can only be added, if the dimensions of both matrices are the same. When two matrices…

Q: Show that the vectors (4-3) and (5,2) form a basis CF TR

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Q: Find the magnitude of the vectors represented 3 by (@5 0² 05 + !|

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