Prove in general that orthab is orthogonal to ā.

Q: Suppose A and B are non-zero vectors in R. If A•B = 0, then A and B are parallel. True False

A: Follow next step

Q: Prove that if A and B are orthogonally diagonalizable then so is A + B.

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Q: For each of the following bilinear forms b : V × V → R, state whether b is product and explain why.…

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Q: Let A = 3 2 1 -14 -5 -2 12 -4 -3 a) Beside the origin, does A fix any other vector? -5 b) Find the…

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Q: -- Compute the orthogonal projection of v = 1 onto the line L through 4 and the origin. 7 projz (v)…

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Q: Suppose u and v are unit vectors and their dot product is -0.2. Find all real numbers c such that cu…

A: It is given that, u→ and v→ are unit vector and u→.v→=-0.2 it is also given that,  cu→+v→ and u→+cv→…

Q: 1.2.5 If a, b, and c are linearly independent vectors in R", prove that a+b, b+c, and a + c are also…

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Q: . If u and v are nonzero vectors in Rº, why do the equa- tions u · (u x v) = 0 and v · (u x v) = 0…

A: The dot product of orthogonal vectors is equal to zero.

Q: Suppose v1, v2, v3 are vectors in Rn, and that u and w are both in Span{v1, v2, v3}. Prove that for…

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Q: Given vectors v1 = 1 2 1 v2 = −2 1 2 and v3 = −1 3 3 in R3 , determine if w = 5 5 1 can be written…

A: Linear combination of vectors

Q: (2) Prove that if a + b and a – b are orthogonal, then a and b have the same magnitude.

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Q: 7.8 Prove, by writing it out in component form, that (a × b) × c = (ac)b — (b. c)a, and deduce the…

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Q: b. If Ax has a zero entry, then A has a row of zeros.

A: Given:- Ax has zero entry

Q: . Prove that for any two vectors d and b in R³, there exist two vectors bí and b such that: T = 6 +…

A: The vectors a→ and b→ lie in the 3 dimesional axes.Any vector is a sume of two vectors.Thus,…

Q: Problem 2 (a) subspace of R32? (b) For which real value(s) of c, if any, do the vectors 3 and (c)…

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Q: Suppose u, v, and w are vectors in R³ and W = span{u,v,w}. Let x be a vector in R³ that is…

A: We are given that x is orthogonal to each of the vectors u, v, and w. Thus, x is orthogonal to any…

Q: Given the vectors A = 3i – 5j + 2k and B = 7i + j – 2k. Find the vector projection of A onto B.

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Q: 2. In Euclidean geometry with standard inner product in R³, determine all vectors v that are…

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Q: -). The vectors U = (c²/3, b, 3), V=(√c, 2, 1) are parallel. Find the norm of the vector U.

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Q: 20. Prove = [-2,5, 1], [2,1, -1] and w = = [-6,0, 12] are orthogonal. -

A: Let three vectors a→ , b→ , c→ If these vectors are mutually orthogonal then  a→.b→ = 0 b→.c→ = 0…

Q: Given the vectors u (1,1,-2), v = (1,1,1), and w-(-1,1,0) a. Show that these vectors form a mutually…

A: Questions regarding orthogonality of vectors in the three -dimensional space over real numbers

Q: Prove Theorem .Let Q be an orthogonalmatrix. detQ=+-1

A: Given that, “Q” be an orthogonal matrix, So, QQT=I=QTQ…