Let 7 and w be vectors in R". Prove that If |7| = |7| = | 7 + |, then |7 - wf=3|7

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: ii) Show that any four vectors oj, , 5, Vi in R are linearly independent.

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Q: Determine k so that the vectors (1, –1, k – 1), (2, k, –4), (0, 2, + k, – 8) in R³ linearly…

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Q: If AB = 0, the columns of B are in the nullspace of A. If those vectors are in R”, prove that…

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Q: Prove the property if a and b are vectors and m is a real number.0 . a = 0

A: Given: If a and b are vectors and m is a real number. To prove: 0·a = 0

Q: 5. Determine the number of vectors (x1,...,x„), such that each x; is either 0 or 1 and i=1

A: (x1,x2,...,xn) is a vector with xi is either 1 or 0.  Now, ∑i=1nxi ≥ k implies at least k of the…

Q: Find a vector v satisfying 3v + (5, 20) = (11, 17).

A: To find a vector v satisfying 3v+(5,20)=(11,17).

Q: Which of the following cannot be defined as an inner product between two vectors (x0, Yo) and (¤1,…

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Q: Find a nonzero vector c in R^3 such that Ax=c is consistent.   A = 2 1 1 0 -2 -2 2 4 0 -1 3 0

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Q: C. If a =.Find a vector b such that compab = v2. %3D

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Q: Prove that if x and y are vectors in R", then |||x|| – ||y||| < ||x- y||. X

A: Given x and y are vectors in Rn we have to prove that x−y≤x−y Since, x=x Hence,  x=x−y+yAdd and…

Q: 5. a) Prove that -2-M u-+ for all vectors in R". b) Explain parts a) geometrically.

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Q: 21. Use vectors to prove that (a² + b³)(c² + dď²) = (ac + bd)² for any four numbers a, b, c, and d.…

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Q: 1. Show that the set as; S = {(1,1,1), (2,3,3), (0,1, 2)} spans R3, write the vector (4, 6, 7) as a…

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Q: 1. Prove that if u and v are vectors in Rn, then |u·v| s ||u|||v|| where ju v| denotes the absolute…

A: As per guidelines we have to attempt only 1st question

Q: Suppose that u and v are vectors in 3-space such that u ||= 5 and u · v= 7. Find: (a) u · u = (b) v…

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Q: Determine whether the given vectors (1, 1,-1, 1), (1,-1, 2,-1), (3, 1, 0, 1) in R* are lincarly…

A: Given vectors are: (1, 1, -1, 1) , (1, -1, 2, -1) , (3, 1, 0, 1) We have to determine whether the…

Q: If a and b are two vectors in 3-space, then axb bxa. Select one: O True False

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Q: 7. Prove that if A and B are any vectors, then the vectors BA + |A|B and B|A- JA|B are orthogonal.

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Q: Show that if R" = Span(v1, v2, · .· Vk) for some vectors v; of R" with k > n then one can find n…

A: Given:           If            ℝn = Span(v1,v2,..........vk) for vi of ℝn  with k&gt;n, Prove:…

Q: 4. Determine whether the given vectors form a fundamental set on the interval (-0, 00). -()-. X1 =…

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Q: The vectors u = (-7, 1, -2) and v = (-28, x, - 8) are parallel if and only if x = - 212 %3D Select…

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Q: 2) How many different vectors are drawn here? -/

A: 3 vectors are same which has same direction and magnitude and other 2 vectors are same in direction…

Q: Determine n so that the vectors m = (-2, 1, k + 1) and n = (0, 2, -3) are parallel but in the…

A: It is assumed that the question asks to find the value of k for which the vectors will be parallel…

Q: nay construct orthogonal vectors a an V such that for each k

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

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Q: When V is spanned by {v1, v2, . . . , vk} and one of these vectors can be written as a linear…

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Q: If dim(V) = n, then there exist a set of n+1 vectors in V that will span V. Select one: O True O…

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Q: Prove that A•(AxB) =0. Note that A and B are vectors.

A: Prove that A•(AxB) =0. Note that A and B are vectors

Q: a Let V be the set of vectors of the form b,where a, b, c are real numbers, then V is not closed…

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Q: If W is the set of all vectors of the a form 0, where a is a real [B] -1 number. Then, which of the…

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Q: H is the set of all vectors x = X2 in R³ with the property that X3 X1 + x2 = 0 and Xi – x2 + x3 = 0.…

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Q: 50 Express the vector b = – 11 as a linear combination of the %3D – 48 - - 14 5 - 10 - | - vectors…

A: the question are based on the concept of linear combinations. we will form the system of linear…

Q: Determine a particular vector z3 so that the following set of 3 vectors are independent: a Z2 = 23 =…

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Q: 3. Find the set of vectors in R³ which are orthogonal to both (4, 2, 0) and (3,6,9).

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Q: Suppose V={v1,v2,...,vn} is a set of nonzero vectors, and let                    x= a1v1 + a2v2…

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Q: Determine k so that the vectors (1,–1, k - 1), (2, k,-4) and (0, 2 +k,-8) in R linearly independent.…

A: The detailed answer and explanation is given below:-

Q: Which of the given sets of vectors in R3, with the standard inner product, are orthogonal,…

A: a) Given, 01-1,011,200 Consider the vectors, u=0,1,-1v=0,1,1w=2,0,0 Now find the inner product of…

Q: 12. Let Q C R such that number of vectors in Q is (6) then Q is linearly independent O True False

A: The subset possible with full 6 vectors should be equal to R^6. For Q to be linearly independent its…

Q: (B) If ū and ỹ are two vectors then prove that ū can be written as a vector parallel to v plus a…

A: given that ,  u→ and v→ are two  vectors

Q: 7) Find all vectors v in F such that 2v + ) -)

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Q: What conditions must a and b obey in order to make all vectors u = (ui uz uz)", such hat and bu to…

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Q: Suppose that u and v are vectors in 3-space such that |u||= 5 and u · v = 7.

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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.

Q: 7. If î, ĵ and k are the standard unit basic vectors in 3-space, determine the value of: k· (j – 3k)…

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Q: Let a, b, and c be n-vectors and let k be a real number.(a) Show that a · b = b · a.(b) Show that (a…

A: Given, Let a, b, and c be n-vectors and let k be a real number.(a) Show that a · b = b · a.(b) Show…

Q: 7) Three different vectors in R2 that have a norm equal to 5 are:

A: In the given question we have to find three different vectors in ℝ2 that have norm equal to 5.

Q: Find a vector b such that compab = 2. If a = ⟨3,0,−1⟩

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Q: 1. Consider the vectors x¡ = (8, 6)' and X2 = (4, –1)' in R?. %3D (a) Determine the length of each…

A: (a)