Find scalars a, b, csuch that au + bv + cw = = (-6,12,4) u = (-1,0,2), v = (2,2,–2), w = (1,–2,1)

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: 2- We can write the vector x = (19,–1,–) in R³ as a linear %3D combination of the vectors x1 = (4,2,…

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Q: Find a vector a with representation given by the directed line segment AB. A(0, 4, 2), B(4, 4, –1)…

A: Given vectors

Q: What is the size of the space stretched by the vectors {(1,0,2),(2,1,4),(1,-1,1)}?

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Q: Let u1 = (-1,1,3), u2 = (2, 1, –3), uz = (3,0, 1) are three vectors. %3D Find expansion of the…

A: We have to write in linear combination form

Q: (-2,3,1,0,2). Find scalars a and b so that аи + bv 3 Let u = (2,1,0,1, –1) and v = (-8,8, 3, – 1,7).

A: u=2, 1, 0, 1, -1  &  v=-2, 3, 1, 0, 2

Q: The vector (-1, 5, 3) is orthogonal to vector : Select one: О а. (0, 1, -2) O b. (-1, 1, -2) О с.…

A: Two non-zero vectors are orthogonal to each other if their dot product is equal to zero.

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: (i, 2, 3i), v = Co over C. Are these vectors linearly independent? Can they form a basis 5.…

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Q: 3. Show that the vectors v, = (0, 3, 1, -1); v, = (6, 0, 5, 1); v; = (4, -7, 1, 3) form a linearly…

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Q: What is the scalar projection of á = (1,0, 1) onto b = (0, 3, 4)?

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Q: FBShow that the vectors (taken from a vector consisting of all functions of the real numbers) are…

A: The objective is to show that the vectors are linearly independent.

Q: Which of the following vectors is the scalar multiple of z-(4, 3, -2) ? Ou- (-28, -21, -14) Ou-(-24,…

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Q: Find the projection of ū = (2, -3, 1) onto v = = (-3, 0, 1) %3D 3 0, А. B. (3.0. -1) В.

A: u→ =2, -3, 1v→ =-3, 0, 1v→ =(-3)2+02 +12       =9+1|v→| =10    u→  · v→ =2, -3, 1·-3, 0, 1u→  · v→ =…

Q: 9. Find orthogonal projection of u=(-1, 2, 5) in the direction of v=(3, 1, -2).

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Q: Find a vector a with representation given by the directed line segment AB, where A(-4, 0, 1) and…

A: A=-401,  B=18-1 the vector a is given by  a=B-A

Q: 3- Suppose that A = {x1 = (2,1,3), x2 = (2,0,1), x3 = (3,0,4)} then [A] = R3, then the scalars we…

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Q: Let u = (2, 1, 5) and v = (3, 4, 2). Find the scalar and vector projections: comp,u, uv

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Q: 3. Show that the vectors v = (0, 3, 1, -1); v, =(6, 0, 5, 1); v, = (4, -7, 1, 3) form a linearly…

A: Given the three vectors

Q: Find the coordinate vector of [4, -2, 1] relative to the ordered basis B= ([0, 1, 1], [2, 0, 0], [0,…

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Q: Find all vectors u such that ux(1,1,1)=(8,-5,-3).

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Q: (2,1, –4,0), v = (-1,-1,2,2), and 19. Find two vectors of norm 1 that are orthogonal to the vectors…

A: We have to find the basis of these vectors, which are independent. A=2-131-12-425024~I4 and they all…

Q: 3. Show that the vectors v = (0, 3, 1, -1); v, = (6, 0, 5, 1); v3 = (4, -7, 1, 3) form a linearly…

A: Given vectors are: v1=(0,3,1,-1), v2=(6,0,5,1), v3=(4,-7,1,3)

Q: The plane that contains the points (-2,1,0), (1, 0, –1) and (0, –1, 1) is orthogonal to which…

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Q: In each part, use a scalar triple product to determine whether the vectors lie in the same plane.…

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Q: 1. For non-zero vectors, a and b, show that axb =a5-(ā • 5} . %3D

A: For non-zero vectors a→ and b→ we have to show that: a→×b→2=a→2b→2-a→·b→2 Assuming, a→=ib→=j Putting…

Q: Find orthogonal projection of u=(-1, 2, 5) in the direction of v=(3, 1, -2).

A: find the orthogonal projection of u=-1,2,5 in the direction of vector v=3,1,2 it is known that…

Q: The vectors [1, 0, 1], [1, 1, 1] and [1, 0, -1] are coplanar. True False

A: Using coplanarity conditions we have

Q: Find the scalar and vector projections of d = (4, 2, –5) on b = (3, –1, 6).

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Q: For what values of the scalar k are the three row vectors (k,1,0), (1,k,1) and (0,1,k) linearly…

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Q: (1,2,3) and Question 3. Evaluate the cross product of the vectors u = =(-1,0,2). Also evaluate (u ×…

A: Given u= <1,2,3> and v=<-1,0,2>  Find u×v and (u×v).v

Q: Find a basis for the set of vectors in R^3 in the plane 3x - 2y + z = 0. Also state the dimension.

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Q: Find both the scalar projection and the vector projection of b onto a, where a = (3, -3, 1) and b =…

A: Consider the given vector: a=3,-3,1b=2,4,-1 Here, the objective is to find the scalar projection and…

Q: 2. Consider the vectors [2, 1,0, 0], [3, 1, 0, 0], [0, 0,0, 1)] in R'. Find a vector v so that v,…

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Q: 2- We can write the vector x = (19,–1, -) in R³ as a linear combination of the vectors x1 =…

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Q: Suppose {v1, v2, ..., vp} is an orthogoal set of vectors. Show that {c1v1, c2v2, ..., cpvp} will…

A: Since {v1, v2, ..., vp} is an orthogoal set of vectors, dot products between any two of them will be…

Q: nd scalars a, b and c such that a(2,0,1) +b (1,3,2)+c(1,0,1)=(7,3,4)

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Q: Find orthogonal projection of v=(3, 1, -2) in the direction of u=(-1, 2, 5).

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Q: Find a vector of norm 1 that is orthogonal to the three vectors u = (2,1,-4,0), =(-1,-1,2,2),…

A: The solution is given as

Q: 1. Find all unit vectors that are parallel to the line going through the points (1, 3, – 1) and (2,…

A: Since you have asked multiple question,as per our guidelines we are supposed to answer only one…

Q: Show that the vectors (1,1,0), (1,0,1), and (0,1,1) generate F3.

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Q: 9. Determine if the vectors å = [-1, 2, 1], b = [-2,4, 2], and ở = [12,8, 1] are coplanar. %3D

A: given vectors a=[-1,2,1] b=[-2,4,2] c=[12,8,1]

Q: 6. Find a unit vector that is orthogonal to both [0, 1, 1] and [1,0, 1].

A: We will find the unit vector orthogonal to both the vectors as following.

Q: Find the scalar product of x and y x =(-1, 0, 2) and y =(-7, 7, 3)

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Q: Find a vector b such that compab = 2. If a = ⟨3,0,−1⟩

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Q: Consider the plane x1 + 2x2 + x3 = 0 with basis S = {(-1,0, 1), (-2, 1,0)}. If (x)s = (2, -1), find…

A: In this question, we need to find the vector x on plane for the given condition.

Q: The scalar projection of the vector 7 = (-2, 3, 1) on 7= (2m, -1, 3) is -1. Determine the value of…

A: Follow next step

Q: Find the scalar and vector projections of b onto a. (4, 7, -4) ь 3 (3, -1, 1) a

A: a=4, 7, -4, b=3, -1, 1 1. Scalar projection of b onto a is Proj ba. Proj ba=b·aa          =3, -1,…

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.