Find all vectors in R* that are orthogonal to both 1 1 V1 = and V2 2 -2

Q: Find a unit vector orthogonal to both u = (1, -2, 1) v =(2, 1, 0)

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Q: An inner product (•, ·) on R³ under which the vectors 1 Vị = 1 1 , V2 = 2 satisfy (v1, v2) = 0…

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

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Q: 2. Show that if the vectors v,, v2, .,Vm are mutually orthogonal then they are linearly ...…

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Q: 8. Let C = 2 c=(; 1) - (;) ()- and b = Find a 2-vector z such that Cz = b.

A: we have  C=112-1b=11   we have to find a 2-vector such that  Cz=b

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

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

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Q: Which of the following vectors is coplanar to [1, 1, 1] and 2, 3]?

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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: The two vectors u=(-2,3,1,4) and v= (1,2,0, -1) are orthogonal in the vector space R4 True False

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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: 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: ): 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: Find a nonzero vector orthogonal to the plane through the points P, Q and R if P(1,0,0), Q(7,8,0)…

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Q: 10) Find two vectors of norm 1 that are orthogonal to the vectors u = and

A: Consider the provided question, u=12-23 and v=2134 Let w=ABCD be such a vector,Then, w·u=0…

Q: Find the scalar and vector projections of b onto a, where a=⟨−1,1,2⟩ and b=⟨−1,5,4⟩

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Q: ^2

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Q: Determine all vectors v that are orthogonal to u.u = (4, −1, 0)

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Q: ) Show that the three vectors vị = (1, 2, 3, 4), v2= (0, 1, 0, – 1), and v3 = (1, 3, 3, 3) form a…

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Q: Let x 0 and y 0. (a) If xly, show that {x, y} is a linearly independ- ent set. (b) Extend the result…

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Q: Let x and y be two orthogonal vectors. Then prove that +

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Q: 3. Use the Wronskian to determine whether the functions fi = e*,f2 sinx and f3 = x are linearly…

A: To find- Use the Wronskain to determine the functions f1 = ex, f2 = sinx and f3 = x3 are linearly…

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

A: Now let

Q: Q2. (d) Show that u=(-2,3,1,4) v=(1,2,0,-1) and are orthogonal vectors in R4.

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Q: Find all values of the scalar kfor which the two vectors are orthogonal.

A: Given: u=23, v=k+1k-1 Concept Used: If two vectors are orthogonal then their dot product is zero.

Q: Find the scalar and vector projections of b onto a, where a = (-1, 1, 2) and b = (-2,7,2). 1. comp,…

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Q: 1 Find two vectors of norm 1 that are orthogonal to the vectors u = and v = 3

A: Given problem is :

Q: orthogonal to the vectors

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Q: Find non-zero vectors I and 7 that are both orthogonal to and orthogonal to each other.

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Q: Let L be the line in R that consists of all scalar multiples of the vector 2 Find the orthogonal…

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Q: 4. Show that the vectors v1, v2, and v3 are linearly dependent, where Vị = V2 = and v3 =

A: If we have a set of vectors v1, v2, v3, ..., vn, then they are said to be linearly dependent if…

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

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Q: 6. Let x#0 and y‡0. (a) If x 1 y, show that {x, y} is a linearly independ- ent set. (b) Extend the…

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Q: Let x = (1,2,3) and y = (1,1,1) Project y on x (in econometrics, this may be denoted by Px). Are the…

A: We will first write the formula for projection of a vector onto another vector b .

Q: Find basis for the set of vectors in R2 on the line y= nx . where n=9.

A: Explanation of the solution is given below...

Q: . Let x and y be two orthogonal vectors. Then prove that

A: If x is any vector then Euclidean norm or 2-norm is denoted by ||x||2 and is given by  ||x||2 =…

Q: are vectors in R³ are linearly independent but ü,v,w are linear dependent. Show that there exist…

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Q: Let a = 2i and b = -2i + 3j be two-dimensional vectors. Compute la – b|.

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Q: Find all vectors in R2 that are orthogonal to u = (2,1).

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Q: Find a linear mapping G that maps [0, 1] x [0, 1] to the parallelogram in the xy-plane spanned by…

A: Given: The maps [0, 1] x [0, 1] to the parallelogram in the XY-plane spanned by the vectors (2, 3)…

Q: There are 6 linearly independent vectors in R°. O True False

A: We know that the dimension of the vector space R5 is 5.

Q: Find the orthogonal projection of the vector b =-1 on Nul(A), where -2 -2 3 -10 A = 1 -1 2 3 1 -3 3…

A: For the solution follow the next steps.

Q: Find an equation of the plane that passes through the point P(4, 5, 3) and has the vector n = (1, 8,…

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Q: saly dla Determine whether the vectors v1=[12 1]^T, v2=[10 2]^T and v3=[5 6 7]^T are Linear…

A: Given vectors: v1=[1 2 1]T=121 v2=[1 0 2]T=102 v3=[5 6 7]T=567

Q: prove that 1 Ə div A; = {√g grk Ak} = div A¹, Əx* where A; and Ai are the covariant and…

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Q: Show that the vectors (1- i, i) and (2, –1 + i) in C“ are lincarly dependent over C but linear…

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Q: Find a so that the vectors v = i- aj and w = 7i + 7j are orthogonal. ..... une on integer or o…

A: If two vector orthogonal then dot products will be zero