Let E be a Euclidean space with inner ratic form. For all u, v E E, we have the C y(u, v)² ≤ $(u)(v), if u and v are linearly dependent.

Q: 1. Define the vectors and as below, ²-[3] *-3 (a) Show that the vectors form a linearly independent…

A: The given vectors are  u→=2-1, v→=13 We have to show that the vectors form a linearly independent…

Q: Suppose V1, ..., Vn are vector spaces then does L(V1 x...x Vn, U) have the same dim with L(V1, U)…

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Q: Suppose that the set A ={X₁, X2..., Xn}, X₁ ER" spans the entire space R", i.e. for any arbitrary n…

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Q: If able please provide a visual representation , this question is from linear algebra: Let P and Q…

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Q: Is the set V = {(x, y) x >0} where (x1, y₁) + (x2, Y₂) = (x₁x2, y₁ + y₂) and c (x, y) = (x,cy) a…

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Q: Let V be a vector space, T a linear operator on V, and v, w E V. Suppose that T(v + w) = v – 2w and…

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Q: Consider two bases B= (b, b2) and C= (c, c2) for a vector space V such that b, =e, - 6cz and by =…

A: Given two bases  and  for a vector space V such that and . Also, given that and we have to find .…

Q: (a) Give examples of three distinct vectors v1, v2, v3 in the vector space R3 such that v2 E…

A: Let v1 = {1,1,1}v2 = {2,3,4}v3 = {1,2,3} Here v2 = {2,3,4} = {1,1,1}+{1,2,3} = v1+v3

Q: Let V be an n-dimensional vector space. Define f: V→ R by f(v) = |v|". Let p,q E V.Find d fp(q).

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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. Define the vectors u and 7 as below, *= [3] B (a) Show that the vectors form a linearly…

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Q: Let S = {a+bx+cx²: = {V1, V2, V3} and T a, b, c = R}, where v₁ = 1 + x + 3x², v₂ = −2 − 2x – 7x², v3…

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Q: If T is defined by T(x)=Ax, find a vector x whose image under T is b, and determine whether x is…

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Q: Let u = 4 h = V= and w= 1 . For what value of h is w in the plane spanned by u am

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Q: Let u be a linear combination of {1₁, 1₂, 13). Select the best statement. A. span{u₁, U₂, U3} =…

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Q: Let S = {x3, x² + 2x, x² + 1}. Is S is span(P2(x)) or not? Let T = {(2,-2,4), (3, -5,4), (0,1,1)}.…

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Q: 2. Let W1 and W2 be two subspaces of V, such that dimg(W1) = dimg(W2) = 2. Suppose that the only…

A: here we can use linear combination to prove that given set is linearly independent.

Q: : Let V be the set of all ordered pairs of real numbers (u1, u). Consider the following addition and…

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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: Q2. In the vector space V = R°, if we take a set: S = {(4,5, 6), (k, 5, 1), (4, 3, 2)} %3D Find the…

A: In the vector space V = R3 , if we take a set S = { ( 4, 5, 6 ), ( k, 5, 1 ), ( 4, 3, 2 ) }. Then,…

Q: 19. Prove that Edin H(d) log" d = 0 if m 1 and n has more than m distinct prime factors. (Hint: use…

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Q: Describe all possible ways in which two planes (passing R3 could intersect. Suppose V is a vector…

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Q: Let ū = (3,2), v = (-2, –2), and w = (-4,3). Find the vector x that satisfies 5u – v +x = 7x + w. |…

A: Given that u→=3,2v→=-2,-2w⇀=-4,3

Q: Let X and Y be points in R³. Let P be a point on the line segment joining X and Y such that the…

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Q: Prove that if (V1,V2, V3} is linearly independent, then so too is the set (u,u2, u3} where u, vı-…

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