Let u1 U2 = -1 Uz = then write x as sum of two vectors on in span {u1} and other one in span {u2, U3,} 1 -2 (a) (b) - - -2 (c) (d) -3 110 123

Q: Find the unit vector in the direction of <4,2>

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Q: express vector as a product of its length and direction. 1/(3)^1/2 i + 1/(3)^1/2 j + 1/(3)^1/2 k

A: Let the given vector is: v=13i+13j+13k

Q: mine the (smaller) angle between the two ve Sa - 7a +4a 0 r Ф 2a + a - 3a 0 1 Ф

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Q: A = [-2,4,-2,-4,        2,-6,-3,1,        -3,8,2,-3,        0,2,5,3]  Find a non-zero vector R^4…

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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: Write N(A) as the span of a vector (r vectors). What is dimN(A)? Why?

A: Null space, N(A) is the set of all vectors x in R^4 here, which are solutions of the equation Ax=0,…

Q: find the diJ tance betueen the vectors

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Q: Consider three vectors A 6) (a) Find A (B+C). Fnl A C) Find A (8C) i Find Bx(A-C)

A: Here we have  A=4i+6j-2kB=2i+7j-kC=0i+3j+5k i) find A·(B+C) ii) find A·(B×C) iii) find A×(B+C)

Q: Let -BHGH) V₁ If possible, express was a linear combination of the vectors ₁ and ₂2. Otherwise,…

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Q: Check that the space generated by the vectors (1, 3, 5), (1, 4, 3), (1, 1, 9) is equal to the space…

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Q: Determine whether the vectors (1,2,3), (5,6,7), (9,10,11), and (4,8, 12) are linearly independent.

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Q: Write the vectors (1, 0, 0) and (0, 0, 1) as linear combinations of vectors {(1, 0, -1), (0, 1, 0),…

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Q: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOS S =…

A: According to our guidelines we can answer only three sub-parts and rest can be reposted.

Q: The normal vector of 2x + By - 16.7z = -8 is: ○ [2, 뮤, -16.7, 8) ① [호, 꽃, 16.7, -8] ① [올, 꽃, -16.7]…

A: We have given equation of a plane  92x+133y-16.7z=-8 Comparing this with the equation  lx+my+nz=d We…

Q: Find a vector orthogonal to both ⟨1,−10,0⟩ and to ⟨0,7,4⟩ of the form

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Q: Find u v. = (9, 2) v 3 (-8, 4) V: U V D

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Q: Verify the identity Ax(BXC) = B(AC) - C(A-B) using the following vectors A = ax + 2ay + 3az B = ax…

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Q: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

A: we will write the given vector as linear combination of vectors in as and find the unknown…

Q: Solve for all vectors X so that × X = .

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Q: Find a unit vector in the direction of

A: Given that,   vector = <6, 3, 2> = u¯ (Say)   Unit vector = u¯u = <6,3,2>62+32+22 =…

Q: Q3/A/ If ā = i – 2j + k , Find: i) (ā x b). (ā x c) ii) (ā × 5) × (ā x c) tho vectors 2i - i+ 2k and…

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Q: (d) comp5 (e) projzā

A: Here we want to find component of vector b along the vector a . And  Projection of vector a along…

Q: why is it not all 4 vectors span W?

A: Lets look at how span of a set is defined :

Q: Find the length of the vector x = [-2, 2, 6 ]

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Q: :) What is a 2b2+|a.b|²? Let a = 0 and b = -2 0 2 be two vectors.

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Q: Suppose that u₁ and u2 are vectors with ||u₁|| = 2 and ||u2|| = 3. You are also given that u₁ · U₂ =…

A: Given that  and  are vectors such that .Given that  and  for .We need to find  for .We need to…

Q: Let S be the set of vectors in R4 (S = {V1, V2, V3, V4, V5}) where, V1 = (1,2, −2, −1) v₂ = (-3, 0,…

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Q: v,w,x ∈ℝ^7 are non-zero vectors. Which of the expressions do and do not make sense. (v+w)/x w-(v⋅x)…

A: It is given that v→,w→,x→∈ℝ7 are non zero vectors. The objective is to determine which expressions…

Q: 17. Find the unit vector ofd = [–3, -7, 4]. a) [-3,-7,4] b)=[-3,7,4] 7 4 示

A: Since this is a multiple question, according to the Bartleby answering rule, only the first question…

Q: Find Vector A and B such that A is parallel to , B is perpendicular to and A + B =

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