5 Suppose that u = 1 2 and v= 0 are vectors in R³. Determine the smallest 2 --- 2 subspace H of R³ that contains the vectors u and V. Is the vector w= in H?

Q: 4. Express PQ-RQ+SR-PS+RS as a single vector.

A: Expression

Q: V4. Consider the following two sets of Euclidean vectors: 3x + 2 y + 4 z = 0 y? + 3 x = 3 z Explain…

A: The solution is given as

Q: Consider V = R^3 and U consists of those vectors each of whose first component is non-negative.…

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Q: i) Using Gaussian Elimination method, verify that x, = 2, x2 = -1, and x3 = 3. ii) Show that b is in…

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Q: Determine if the list ( [111], [121], [011], [122] ) of vectors from vector space V = R^3 is…

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Q: Calculate r'(t) and T(t) and evaluate T(1). r(t) = (6 + 7t,12,5 – 1²) (Give your answers using…

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Q: Find a nonzero vector c in R^3 such that Ax=c is consistent.   A = 2 1 1 0 -2 -2 2 4 0 -1 3 0

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Q: Find all the vectors of the family (2-jx, j4, 2-j5, jx) that are of hermitian length equal to 21.

A: Let Y=2-jx,j4,2-j5,jx Length =Y=4+x2+42+4+25+x2   Y=49+2x2 49+2x2=2149+2x2=2122x2=392x=±14

Q: Prove that the vectors (a1, a2), (B₁, B₂) = R× Rare linearly dependent iff α₁ß2 - α2ß₁ = 0.

A: The given vectors are  and We have to show that the given vector is linearly dependent if

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…

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: 1] Determine whether the first vector is a linear combination of the other vectors. (c) (-1, 15);…

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Q: Let the vector 3i +j can be expressed as a sum of vectors u and v where u is parallel to the vector…

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Q: Determine whether the vectors v₁ = (1, 6, 0, 0), v₂ = (0, -1, 0, 1), v3 = (0, 0, 1, 1), and v₁ = (1,…

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Q: Show that the vectors 2 -2 2 uj = 2 uz = 3 uz = 7 1 -5 -3 are linearly dependent. Find all r1, x2,…

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Q: Prove that a set of non -zero vectors {x1,x2,...,xn) is linearly dependent if some of these vectors…

A: A set of non-zero vectors {x1,x2,...,xn} is linearly dependent if some of these vectors say xi is a…

Q: Let ?1 = (4 3 2 1), ?2 = (−2 0 -1 0), ?3 = (0 3 0 1) a) Find the subspace of R^4 spanned by these…

A: Note: There are many long answer for subparts in the questions. So I will answer the first two…

Q: Suppose V,W are subspaces of R^n. Let V ∩ W be all vectors which are in both V and W. Show that V ∩W…

A: Suppose V,W are subspaces of R^n. Let V ∩ W be all vectors which are in both V and W.  We have to…

Q: Let a = (7, 10, 1) and b = (10, 3, 6) be vectors. Compute the cross product %3D ахЬ.

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Q: If the cross product of two nonzero vectors is the zero vector, then each of the two vectors is a…

A: Explanation of the answer is as follows

Q: Suppose v1, V2, V3 is an orthogonal set of vectors in R. Let w be a vector in span(v1, v2, V3) such…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find a vector orthogonal to both (-3, 2,0) and to (0, 2, 1) of the form (1,

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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: Find the dimension of the subspace of all vectors in R'whose second and third entries are equal. O…

A: Dimension of subspace is 6. Since dimension of R^7 is 7 and the given subspace has second and third…

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…

Q: Find a non-zero vector perpendicular to

A: