Let u and v be vectors in an inner product spacesuchthat || = 2, |u = 1 and theanglebetweenu and v is 60 . (1) Find 3u+ v

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A: See the solution below.

Q: 4. For vectors v and ū in an inner product space V, prove that u´ projzu and i are orthogonal.

A: v

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A: By Cauchy-Schwarz Inequality for the vectors, we have

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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

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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: XII. Show that the dual vector of the antisymmetric part of the dyadic (1 2 3) A = 4 2 1 1 1 1) is…

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Q: 3. Let v, and v2 be vectors in an inner product space V. Show that ||v + v2||? < (||Vvl+ ||v2||)?

A:

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Q: Verify the Cauchy-Schwarz Inequality for the vectors.u = (6, 8), v = (3, −2)

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A:

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A:

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Q: XII. Show that the dual vector of the antisymmetric part of the dyadic (1 2 3) Ā = 4 2 1 (1 1 1) is…

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Q: Two vectors u and v in space are if and only if u .v = 0

A: Condition of dot product.

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Q: determine projection of the vector b = -1 1 1 on the space generated by the vectors {--E)--[ -[+]}…

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Q: Use Lagrange multipliers to find a vector in 3-space whose length is 4/3 and whose components have…

A: use lagrange multipliers to find a vector in 3-space whose length is 43 and whose components have…

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Q: 49. Show that in the vector space V, (R), the vectors (1, 2, 3), (- 2, 1, 4), (- 1, – 1/2, 0) form a…

A: We prove that the set of vectors form a linearly dependent set.

Q: Suppose that u, u and w are vectors in a real inner product space such that (u, w) = 16, (v, w) = 5,…

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Q: Verify the Cauchy-Schwarz Inequality for the vectors. a = (1, 1, -2), b = (1, -3, -2)

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Q: Suppose that two vectors T and ỹ in R" are orthogonal, meaning their inner product satisfies ·g = 0.…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.