2 2 and u4 -5 1. Let uj = u2 = U3 = 2 Let W1 = Span{u1, u2} and W2 = Span{u3, u4}. (a) Show that the subspaces W1 and W2 are orthogonal to each other. 2 (b) Write the vector y = 8 as a sum of a vector in W1 and a vector in W2. 4 -6

Q: [1 2] 3 6 Let A = Write the vector u = (4,3) as u = u, + u„ where u̟ and un belong to the row space…

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Q: 6. (a) Let u, v, w be three linearly independent vectors in Euclidean Space R^7. Determine a value…

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Q: Question 1 Let W be the set of all vectors of the form a) [α] b where -2a +6b-6c = 0 Lc -3 Determine…

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Q: 2. fu = and v = v1, v2, V3 > are two vectors in 3-space show k that u x v= u1 U2 U3 V1 V2 V3

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Q: If V₁, V2 and v3 are 3 vectors in a vector space V such that -7v₁-9v2 = 0. V, and v₂ are linearly…

A: Given that v1, v2, and v3 are 3 vectors in a vector space Vsuch that -7v1-9v2=0. Then v1, v2,and v3…

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Q: The two vectors u=(-2,3,1,4) and v= (1,2,0, -1) are orthogonal in the vector space R4 True False

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Q: Are the vector spaces R4, M2,2, and M1,4 exactly the same? Describe their similarities and…

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Q: EXAΜPLE2 Determine whether the vectors vi-(1,-2,3),v2=(5,6,-1),v3-(3,2,1) are linearly independent…

A: Given vectors are v1 = (1, -2, 3), v2 = (5, 6, -1), v3 = (3, 2, 1)

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A: There are three different reason why the set of vectors is linearly dependent  If a set contains a…

Q: Determine which set of vectors is linearly dependent (a) (b) , (c) (d) (e) (f) O (a) O (b) O (c) O…

A: Recall:A set of vectors is said to be linearly dependent if the determinant is zero.If the…

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Q: Q-2: a) combination of the vectors X = (1,2,3,0) and Y = (2,1,6,0). b) a linearly independent set of…

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Q: (2) Determine if the vectors are linear independent or linear dependent. Justify your answer. (a)…

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Q: Let V1, V2, V3 be vectors in R³ given by 1 »-(;) · ~ -(:). = 6 V2 = 2 2 0 The set {V1, V2, V3} is…

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Q: Are the vectors V₁ = 2 1 1 V₂ = 1₂V3 3 4 1 linearly independent? -9

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Q: (i) Let {u, v} be linearly independent vectors in a vector space V. Determine whether set {v – u, v…

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Q: What is the dimension of the vector space spanned by the vectors v1, v2? v1 = (6, -2, 4) and v2 =…

A: v1 = (6, -2, 4)  v2 = (14, 2,8)  There does not exist any real number c such that v1 = c v2 hence v1…

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Q: Let j TE 2 --- = 1 and u = = Write y as the sum of two orthogonal vectors, #₁ in Span{u} and 2…

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Q: Ui=(1, 1, 1, -1) Uz=(5, 1, 1, 1) Uз-(-3, -3, 1, -3)

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Q: Use matrix multiplication to find the orthogonal projection of (-8, 5, 7) on the xy-plane. Let T…

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Q: Let B' = {u1,u2} and ß = {v1,v2} be ordered bases for a 2-dimensional vector space V. Given that [u1…

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Q: →→→ Let x, y, z be vectors such that x X X y x z →→ = a; y x ➜>> Z X X y = b and ° {(+5) x = -(-+)}…

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Q: 9. Determine whether the vectors v₁ = (1,1,2), v₂ = (1,0,1) and v3 = (2,1,3) span the vector space…

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Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (v2 V1, V1 + V2,…

A: Let us consider the transformation T: V→W defined as T(v)=w where v is preimage of w  and w is an…