1. Let Let W = :x2 + y2 < 1}. (This can be thought of as the collection of points lying either inside the unit circle, or along its border.) Give an example of two vectors in W and one vector not in W. Give an example of a vector u in Wand a scalar, c, for which cu is NOT in W. Give an example of u and v in W, where u + v is not in W. Is 0° in W? а. b. С.

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: Let a = (-3, –4, –4) and b = (2, 2, 4) . Find scalars s and t so that sa + tb = (20, 4, 32) %3D %3D

A: We have to find the values of scalers s and t for a=-3,-4,-4 and b=2,2,4.

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

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Q: According to the formal definition of the term "parallel," two vectors are said to be parallel to…

A: According to the formal definition of the term "parallel," two vectors are said to be parallel to…

Q: If able please provide a visual representation , this question is from linear algebra: Let P and Q…

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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: Q3) A) Let 4 (-1 3, 4) and B (-5, 8, 10) two points in the space, find: 1- The vector AB. 2- Length…

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Q: A vector v in a plane is a line segment with a specified direction, where the component form is…

A: Part(a) Given vector

Q: Show all the work asap

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Q: The sum of the squares of the direction cosines of a vector in space add up to ..............

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Q: 9. Show that is a two-dimensional vector. Ai = -x2 X1

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Q: 1. Letz =1+i,1,=-1+i, locate the numbers z+ z, and , vectorially in the rectangular coordinate…

A: We are Given that : z1=1+iz2=-1+i ⇒z1+z2=(1+i)+(-1+i)=2i and  ⇒z1-z2=(1+i)-(-1+i)=1+i+1-i=2

Q: Let / be the line through the point with coordinates (1,-1,0) in the direction of the vector…

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Q: "ove that if two vectors are linearl y de pendent, e of them is a scal ar mul it ple of the other.

A: Two vectors are linearly dependent, one of them is a scalar mulitple of the other.

Q: 3a) Use the cross product to determine a unit vector that is perpendicular and in the opposite…

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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: 6 2 Show that it is vectors are lineas dependent line or independent.

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Q: Let y = *₁ = 0 and ū= 6 . Write y as the sum of two orthogonal vectors, ₁ in Span{u} and 2…

A: Given that the vectors  y→=0-1-2   and  u→=56-1   .

Q: 4.) Are vectors Linearly independent? 2 3

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Q: Q3 O Let w-l(a,b,c), b= 3a} is Sub Sehoof RE a Sub Spaceef R32 is s w X, = i +2j - K , Xz= -3i+2j-R…

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Q: 5 3 -2 -3 w = -3 |; A= 4 -5 2 2 -5 4 -1 . Determine if vector w is in Nul(A)

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Q: Let u =[3, -1] and v = [0, 1] can you find the vector[h, k] that is not in Span{u,v}? either give an…

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Q: 4 16 -- 12 -21 4. Is the vector in the span of the vectors 10 12 -8 and 8 ? Explain!

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Q: 6. Let a = (1, 0, 3) and u = = (2,-1,5). ) Evaluate projau. Find a vector that is orthogonal to…

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Q: 150. Determine the real number a such that vectors a = -3i+2j and b = 2i+aj are orthogonal.

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Q: 149. Determine the real number a such that vectors a = 2i +3j and b = 9i+aj are orthogonal.

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Q: Let a, b, and c be vectors. Is it a vector, scalar, or is in meaningless? 1) ( a X b ) + a.b 2) -2 +…

A: We will whether the part 1, 2 and 3 are a vector or a scalar or meaningless as following.