Give a non-zero vector in the null space of A. 18 || A = 3 4 1 -4 -4 -4 5 5 1 -3 1 -1 - 4 4 3

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Q: 5. Find a vector æ € R³ such that ||Ax – || is minimal, where [1 1 -2] 1 and b:= 2 1 1

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Q: Let A = 11 -1 -7 -1 5 -1 -7 -1 5 (a) Show that x¹ Ax ≥ 0 for any x € R³. T (b) Find a non-zero…

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Q: Suppose that {x1, x2, x3} is a linearly independent set of vectors in a vector space V . Must {x1,…

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Q: Let V is finite vector space and suppose that V=internal direct sum of U and S1. Also V=internal…

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Q: Why do the set of all polynomials of degree n or less form a vector space, while the set of all…

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Q: -4 8 -2 4. Find a nonzero vector v in N(A), the null space of A, and a nonzero vector w in C(A), the…

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Q: Determine whether w is in the column space of A, the null space of A, or both. 3 7 5 -6 3 1 A = 0 -4…

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Q: Show that λis a root of char(x) if and only if there exosts a non-zero vector v in V with L(v)=λv

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Q: . Let V be a vector space, and {v1, ··· , vn} be a set of vectors that spans V . Show that the set…

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Q: 1 1 1 Let A 1 1 1 1 1 1 3/5 -7/5 is in null(A), or 4/5 Either show that the vector show that it is…

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Q: Let [1 A = 3 1 2 0 1 2 2 Find all vectors in the null space of A. 1013

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Q: Let V be set of all polynomials p(x) = ao + a₁x + a²x² + • anx" for which -5 is a root. Mark the…

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Q: Let 1 0 1 2 3 3 A = -( : )--( * = 0 1 1 02 B = 0 1 1 02 ● 000 00 0 0 1 0 1 Which of the following…

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Q: a non-zero vector in the column space of A. A = -16 -4 0 -16 20 -20 -4 5 -5 20 0 25

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Q: 1. State if the following statement is true or false. The set of vectors B={u= (1.1.4);v=(2,0.2)…

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Q: (6) Suppose that T is a linear operator on a 2 dimensional vector space V and that T+ a I for any a…

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Q: be the vector space of all polynomials of degree 3 or less in the variable z. Let PI(T) 2+x+1²,…

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Q: -1/7 -4 /7 4/7 -5/7 U2 = and 4/7 2/7 2/7 4/7 -4 /7 2/7 03 = Find a vector vá in R* such 2/7 -5/7…

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Q: 6. Let V be a vector space and v1, v2, V3, V4 are vectors in V. Suppose that {v1, v2, V3} are linear…

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Q: Find bases for the column space, the row space, and the null space of matrix A. You should verify…

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Q: 6. Which of the following sets of vectors form a basis for the null space of (1 -1 1 1' 4 -4 3 6 ? 2…

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Q: 8.) Find a vectorx such that 5x-2v=2(u-5x) SOLUTION

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Q: C along with the following operations defined: (a1, a2) + (b1, b2) =(a1 +b1 + 1, az + b2 +1) C •…

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Q: Let A = X = 1 −1 1 1 −1 1 1 -1 1 -1 −1 1 1 1 -1 - Find a non-zero vector x in the null space of A.

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Q: Suppose A E M(R). Write A = (a₁ | |ax). a. A vector x ER is in the null space of A if (select all…

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Q: Let A = -2 -2 5 5 -5 -2 Give a non-zero vector in the null space of A. -5 -2 -1 5 5 1 2

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Q: Find the length of the projection of [−8 −7]onto the vector [−7 5]   Its written vertically…

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Q: = Determine whether w is in the column space of A, the null space of A, or both. W= 3 -1 -3 A = 9 -6…

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Q: Describe the zero vector (the additive identity) of the vector space. P3 x + ]+² +

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Q: Let A = [[3,1,1,2,2],[-3,-2,4,2,2],[-5,5,4,-1,-2]]  Give a nonzero vector x in the nullspace of A.

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Q: Which of the following are axioms of a vector space V? (Select all that are correct.) 1x = x If k,…

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Q: Create a vector a with elements = (-1)" 2n (2n)! 1≤n≤ 100

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Q: Find the norm of a and the unit vector ū in the direction of a if -5 -3 1 -2 |||| i = ||

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Q: Let P2 be the vector space of all polynomials of degree ≤ 2 with coefficients in R, and S= {1 + 2x,…

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