Suppose Q : R? → R is a quadratic form such that Q(x) = 1 for all vectors X E R? Cuch that

Q: Prove that if a is perpendicular to b, then |a +b|^2 = |a|^2 + |b|^2 .

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Q: -21 6. Find h so that the vectors 1 is in the span of the vectors 4, and -3 -0-

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Q: The cross product is not associative. (It is not necessary for | a xb |x c X c to be the x c |.)…

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Q: The following limit lim Select one: O None of them 8x³y³ (z,y) →(1,2) 2x - y O equals 12. O equals…

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Q: Given vectors x, y and z, construct any valid lower-bound for the expression ||x|| || + ||y|| 2 ||.…

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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: The dot product of two vectors can be written in the form s+ 18 t. x1 x2 in R" is defined by * ·ý =…

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Q: Using index notation, prove the following identities among vectors A, B, C, and D: (a) (A x B). (B ×…

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Q: Find the distance d (in the complex plane) between z = 2 + 7i and w = 11 - 10 i. d = √ (1)² + (9)² X

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Q: How many solutions does Ax = [1]   have?

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Q: M3. Which of the following expresses the fact that the vectors u and v have the same length? (a) ū -…

A: M3. The two vectors u and v have the same length if: (a)u→·v→=v→·u→

Q: How does the cross product i x ì relate to the vectors ở and i geometrically? Use this to compute d…

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Q: = If w₁, W2, W3 are independent vectors, are the sums V₁ = W2+W3 and V₂ W₁ +W2 independent or…

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Q: v1 =[ 2 5 1 ] , v2 =[ − 3 1 − 1 ] , b =[ 11 19 5 ] Show that b is in Span{v1,v2}. Express b as a…

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Q: ue or False. Let x, y E R". If || + y = ||x – y||, then x cannot be orthogonal to y.

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