ind k so that the vectors u=(1,2,k,3) and v=( =(3,k,7,-5) in the Euclidean inner product space R4 are orthogonal.

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

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Q: Find two vectors of norm 1 that are orthogonal to the vectors u = (2,−3,4) and v = (3,1,−5)

A: The cross product of two vectors is perpenducular to both of the vectors. The cross product of the…

Q: Let v1 and v2 be vectors in an inner product space V.(a) Is it possible for |{v1, v2} | to be…

A: It is given that,  v1, v2 be the vectors in an inner product space V. a) We have to determine that…

Q: Let V₁, V2, V3 be linearly independent vectors in R". Show that {v₁ + V₂, V₂ + V3, V3 + ₁} is also…

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Q: What should k be if the vectors x=(1,1,k) y=(1,3,1) z=(k,1,3) are in the same plane in the Euclidean…

A: Three vector a1,a2,a3,b1,b2,b3 and c1,c2,c3 will be in euclidean space ℝ3 If  a1a2a3b1b2b3c1c2c3=0…

Q: state a vector with all non-zero entries which is orthogonal to v⃗

A: Given v vector  Let w vector be orthogonal to v vector  Then w vector . v vector = 0

Q: (a) Give examples of three distinct vectors v1, v2, v3 in the vector space R3 such that v2 E…

A: Let v1 = {1,1,1}v2 = {2,3,4}v3 = {1,2,3} Here v2 = {2,3,4} = {1,1,1}+{1,2,3} = v1+v3

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

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Q: cannot be found in such a general cas explain why. In either case, justify you 2) Let a and b be two…

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Q: Find all the vectors of the family (2-jx, j4, 2-j5, jx) that are of hermitian length equal to 21.

A: Let Y=2-jx,j4,2-j5,jx Length =Y=4+x2+42+4+25+x2   Y=49+2x2 49+2x2=2149+2x2=2122x2=392x=±14

Q: Consider the basis B of R² consisting of vectors (-1, 2) and (-6, -3). Find x in R² whose coordinate…

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Q: (×q) × (gxv) + (gxg) x (xv) + (x) x (qxv)

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Q: If V₁, V2 and v3 are 3 vectors in a vector space V such that -7v₁-9v2 = 0. V, and v₂ are linearly…

A: Given that v1, v2, and v3 are 3 vectors in a vector space Vsuch that -7v1-9v2=0. Then v1, v2,and v3…

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: If vectors b, c and d are not coplanc then prove that vector

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

A: Linear Algebra: The vectors are: v1=112-2v2=2112Let denote the vector v3=v1v2v3v4

Q: Find a unit vector orthogonal to both u and v. u = 2i5j + 3k 2-3 V = + -k 10

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Q: Is the pair of vectors 2i – j and -i+jperpendicular? no yes

A: Given vectors 2i-j and -i+j Two vectors are perpendicular if and only if dot product of those two…

Q: Find the length of the projection of 3   onto the vector -3…

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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: ^2

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Q: Find all values of a so that u and v are orthogonal. (Enter your answers as a comma-separated list.)…

A: Since you have asked multiple question, we will solve the first question for you.  If you want any…

Q: What is the dimension of the vector space spanned by the vectors v1, v2? v1 = (6, -2, 4) and v2 =…

A: v1 = (6, -2, 4)  v2 = (14, 2,8)  There does not exist any real number c such that v1 = c v2 hence v1…

Q: Vectors a and b are some vectors in a space with inner Euclidean product, and it is known that…

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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: Prove that the points position vectors collinear. With at 26, 2a-5 and 3a-46 are

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Q: Prove that a(-3,2) and b (2,-3) form basis vectors in xy plane

A: a set is said to be basis if set is linearly independent and it spans the space.

Q: uppose ā and b are two non-zero vectors in R3 and they are not parallel to each other. Then, their…

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Q: Consider A= (0, 4, 2), B =, (6,-1,0) and C = (3, 0, 1). 1 (a) Find the unit vector having the same…

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Q: Let W be the set of all vectors of the form 111 ū= -3s- 2t 2s+t -s-2t Find vectors u and 7 in R³…

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