Please explain why  If V� is a vector space and u� and v� are vectors in V�, then according to the axioms  6v⋅u is also a vector in V� is a false statement

Q: If ū and i are two vectors, prove the identity ld + 레? + |d - 비? = 2| + 2|미2

A: This question is based on vector multiplication.

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

A: Given vectors in space are u and v The vectors cross product is u x v = |u| * |v|* sin(angle between…

Q: ex/IF Ā=i-j+3k and B =2 i+6j+3K Find the vector pricâ+B) and Prj (À-B).

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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: Given three non-zero vectors, a, b & C, is it possible to evaluate a b Explain with an example. •6•²

A: We have given three non-zero vector.

Q: Do question 12 only

A: The given in item #12 is:∫04π​​∫01​∫0x2​xcos(y) dz dx dy Consider the innermost…

Q: Three unique non-zero vectors a, b, and C are defined by four points in space. Select all of the…

A: Proceed as shown below

Q: 10. Write the number of the correct answer Number of vectors in a vector space is 1- any number…

A: Since a vector space cannot be empty, it must contain the additive identity, i.e. 0

Q: True or False? If u and are nonzero vectors, then Span{u, v} contains the line through u and the…

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Q: (x.yız) (x,9e)x4か t. 22 P( 3-1,0) けこくりん)2

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Q: The sum of the squares of the direction cosines of a vector in space add up to ..............

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Q: Are the vector spaces R4, M2,2, and M1,4 exactly the same? Describe their similarities and…

A: We have to determine if the vector spaces, are exactly the same or there is any similarity or…

Q: For any three vectors a, b, and c, we have a x (b x c) (a x b) x c. اختر احدى الدجابات True False

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Q: Is the set of (infinite number of) vectors { (0,0,c) }, where c is a real number, a vector space…

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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: What if the vector v was [ 7, 11, 3]

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Q: 4. a) Givenā = [-5, 2, -3],6 = [7,-4, 1], c = [x, -2, z], and a × c =b, find x and z. b) Find a…

A: Given,  a→=-5,2,-3,  b→=7,-4,1 , c→=x,-2,z

Q: Suppose that three vectors u, v, and w are linearly independent in some vector space. Are the…

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Q: Let a and b be vectors in R" such that ||a||=||||= 2 and <a,b)=3. Then ||a-b||= ..

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Q: The vectors (2,10, 4) and (1, 3, x) are orthogonal if and only if x= -8. Ignore "Give your reasons"…

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Q: Let v1, V2, V3 and u be vectors in R". If u is orthogonal to each of v1, V2, and v3 then u is…

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Q: Which of the following statements is not true for vectors a, b and c and scalars a andB (A) ax (ab)…

A: Here we will  check one by one and then tell about given statments.

Q: 2. Let a, b, c, and d be algebraic vectors in R3, For parts (a) and (b) below, state which theorems…

A: The dot product of the two vectors A→ and B→ is given by the following: A→·B→=||A→||·||B→||·cos θ…

Q: Show that if u and v are vectors in the three-space, then ||u x v||? = ||u|| ||||² – (u · v)²

A: u and v are vectors.

Q: 7. Let +-() वे = -2 and -4 2 3 Find a real number x and a vector such that = -x and 17.

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Q: The vector -3 (GIE) -1 -4 0 -7 vectors -3 2 belongs to the span of the 5 Select one: O True O False

A: Given: W=span-3-10, -1-4-7. To check v=-325∈W.

Q: 5 3 -2 -3 w = -3 |; A= 4 -5 2 2 -5 4 -1 . Determine if vector w is in Nul(A)

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Q: 4 16 -- 12 -21 4. Is the vector in the span of the vectors 10 12 -8 and 8 ? Explain!

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Q: 6. Let a = (1, 0, 3) and u = = (2,-1,5). ) Evaluate projau. Find a vector that is orthogonal to…

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Q: 150. Determine the real number a such that vectors a = -3i+2j and b = 2i+aj are orthogonal.

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Q: Let a, b, and c be vectors. Is it a vector, scalar, or is in meaningless? 1) ( a X b ) + a.b 2) -2 +…

A: We will whether the part 1, 2 and 3 are a vector or a scalar or meaningless as following.