(u x v)• w = UI

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

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Q: The vectors u=(1,-2,1), v=(3,0,-2) and w-(5,-4,0) are: O not coplanar coplanar

A: We can check whether the three vectors are co planar  or not as below

Q: The norm of the vector u = (1, 2, 3, 4) is 30. True O False

A:

Q: Mark each of the following statements true or false:

A: Given,u=4v=5, andu,v=2,   thenu+v=5

Q: Let x and y be linearly independent vectors in R2.If | |x | |= 2 and | |y | | = 3, what, if…

A:

Q: Let u = (4, 2) and v = (2, −2) be vectors in R2 with the inner product ⟨u, v⟩ = u1v1 + 2u2v2. (a)…

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Q: u = (2, 3,-1) v= (0, 1, -2) w = (2, 4, -3).

A:

Q: Suppose that the vectors {v, u, w} are linearly independent in some vector space V. Prove that the…

A: Given that the vectors u, v, w are linearly independent in some vector space V. Then the linear…

Q: Find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and v2 is…

A: v=2i+4j  and  w=-3i+6j. Now, v·w=2i+4j·-3i+6j=2-3+46=-6+24=18 & w=-32+62=45=35 Therefore,…

Q: Show that a set of vectors {v,, v2. ..., V5} in Rn is linearly dependent when dim Span {v,, v2, ...,…

A: We need to show that: {v1, v2, v3, v4, v5}  in Rn are linearly dependent when  dim Span{v1, v2, v3,…

Q: а — Ь Let W be the set of all vectors of the form Find vectors i and v in R' such that W span {u,…

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Q: Prove that u is orthogonal to v - proju(v) for all vectors u and v in Rn, where u ≠ 0.

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Q: Consider the set of vectors S = {2 – x + 4x², 3 + 6x + 2x², 2 + 10x – 4x²} in P2. Show that the set…

A: use linear independent vector definition

Q: Let y = and u = Write y as the sum of two orthogonal vectors, y, in the span of u, and y, which is…

A: Solution

Q: Show that there are no vectors u and v such that 11u 11= 1, ||v|| = 2, and uxv= 3.

A: If u and v are two vectors, and the angle between these two vectors is θ Then the magnitude of the…

Q: Determine all vectors v that are orthogonal to u.u = (0, −4, 3)

A: Given u=(0,-4, 3)we have to find all vectors v that are orthogonal to u,If u.v =0 then vectors u and…

Q: Determine all vectors v that are orthogonal to u.u = (0, 1, 2, −1)

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Q: Show that the vectors 2 -2 2 uj = 2 uz = 3 uz = 7 1 -5 -3 are linearly dependent. Find all r1, x2,…

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Q: Let nonzero vectors ū,v,weR be linearly independent. Show that there does not exist a nonzero vector…

A:

Q: ): Let v = 3 be two vectors in R. and v2 %3D Show that v = belongs to span{v1, v2}. 62

A: We know that if vector "v" is linear combination of "v1" and "v2" then vector "v"belongs to the span…

Q: Suppose that u, ū, and w are vectors in R3 such that ūxi = (2,7, 3) and ūxu = (-5, 4,0). Find: 1.…

A:

Q: Find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and v2 is…

A: we have to find projwv of the given vectors and then we have to decompose v into two vectors, v1 and…

Q: Show that there are no vectors u and v such that llull = 1, llvll = 2,and u·v= 3.

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Q: Suppose v1, ..., vn are linearly independent and Span({v1, .., vn}) = V , then if W ⊂ V and W…

A:

Q: Find Projwv and Decompose v into two vectors v1 and v2​, where v1 is parallel to w and v2 is…

A:

Q: Determine all vectors v that are orthogonal to u.u = (11, 2)

A: Now let

Q: Let u, v, and w be vectors in R^n (that is, u=(u1,u2,........,un) similar for v and w) Prove that…

A:

Q: Show that if u is a vector in R2 or R3, then u + (−1)u = 0.

A: The objective is to show that if u is a vector in R2 or R3 then u + (−1)u = 0. Suppose u and O is a…

Q: Let u = (-1,0,1), v= (3,2, 1) and w = (0,1, 2) . (a) Prove that the vectors u – v, u+ v and u x v…

A: Given : u=<-1,0,1> v=<3,2,1> w=<0,1,2>

Q: 2. Suppose that u, v and w are vectors in 3-space such that ||u|| = 5, u·v = 7, and u · w = -3 а.…

A: Answer

Q: Prove that two non-zero vectors u and v in n-space are perpendicular if and only if u • v = 0

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Q: prove that 12 div A; = √√√x² {√8 8¹k Ax} = dxr div A¹, where A; and Ai are the covariant and…

A:

Q: Prove that for any vectors u, v, and w in R2 or R3, we have u ·(v + w) = u · v + u · w.

A: Let u=u1, u2, u3  ,  v=v1, v2, v3  &  w=w1, w2, w3 be the vectors. Now, v+w=v1, v2, v3+w1, w2,…

Q: Determine whether the set of vectors in P, is linearly independent or linearly depenc S (-2- x, 2 +…

A: The vectors v1,v2,....vk are linearly independent if a1v1+a2v2+...anvn=0 where all ai=0 The vectors…

Q: Determine all vectors v that are orthogonal to u.u = (0, 5)

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Q: Let u, v and w be vectors in Cn . Clearly prove that (u + v) · w = u · w + v · w.

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Q: Show that if u is a vector in R2 or R3, then u + 0 = u.

A: To show that if u is a vector in R2 or R3, then u + 0 = u.

Q: Show that if u + vand ủ – v are orthogonal, then the vectors u and must have the same length

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Q: Let y = and u = 3 Write y as the sum of two orthogonal vectors, one in Span {u} and one orthogonal…

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Q: Let y→=[−8, −7] and u→=[−2, 6]. Write y→ as the sum of two orthogonal vectors, x→1 in Span{u} and…

A:

Q: ): If U, U₁, U₂ are 3 vectors in a vector space V such that 13v₁ = v + 7v₂. Then, u belongs to…

A: It is provided that v, v1, v2 are three vectors in the vector space: V and 13v1=v+7v2. We need to…

Q: Suppose v1, v2, vz is an orthogonal set of vectors in Rº. Let w be a vector in Span(v1, v2, v3) such…

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Q: Let y = 185 || 3 and u = Write y as the sum of two orthogonal vectors, ₁ in Span {u} and 2…

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Q: The vector 1 is in Span{ V2, ., Vm } if and only if ( V1..., Vm ) are linearly dependent. O True…

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Q: Write y as the sum of two orthogonal vectors, x1 in Span{u} and x2 orthogonal to u

A:

Q: Let x, y, and z be vectors in Cn and let α and β becomplex scalars. Show thatz, αx + βy} = α z, x} +…

A: Given: z,αx+βy=αz,x+βz,y

Q: Use the given pair of vectors u = (- 3, – 4) , v = ( – 4, – 4) to compute u + v = u - v = 2u – 3v

A: <a,b> + <c,d> = <a+c , b+d>

Q: Show that (x, y) = 4x1y1-7x2Y2 for vectors x = (x1, x2) and y = (V1 Y2) in R2 defines an inner…

A: