Suppose v, w, z are vectors in R". Show that if r and y are linear combinatio: v, w, and z, then r+ 2y is a linear combination of v, w, and z.

Q: Prove Ảx (B x Č) = B(Ả C) – Č(Ã B) is true by expanding Ả, B, and components (or Cartesian…

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Q: (3) Suppose a vector x is orthogonal to vectors u and v. Show that x is orthogonal to u+v.

A: We will use the fact that x is orthogonal to u and v to prove that x is orthogonal to u+v also

Q: Suppose A and B are non-zero vectors in R. If A•B = 0, then A and B are parallel. True False

A: Follow next step

Q: 02. Approve that the area of the parallelogram spanned by the vectors a= (2, -2, 1) and c= (-8, 8,…

A: Please refer the attached image for complete solution.

Q: 6. If u,v, and w are three vectors in R', describe their linear span.

A: 6. If u,v and w are three vectors in R7, we have to describe linear span.

Q: Consider the collection of vectors --000 1 Is Slinearly independent? Carefully explain your answer.

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Q: Consider the vectors v, = (1 0) and v, = (0 1) in R,. the vector ( 0.4 3.7) can be written as a…

A: Linear combination

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

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Q: Suppose that u, v are vectors in R3 , u · v = 1, ||v|| = 1, the angle between u and v is π/3, and u…

A: The detailed solution is as follows below:

Q: Let x, y, z be (non-zero) vectors and suppose w = 12y – 9x + 2z. If z = 3x – 4y, then w = x+ 4 y.…

A: Vector spinning sets

Q: Assume that the vectors u = ai-j+k and w=i+9j+5k orthogonal. Then the are value of a is

A: If two vectors are orthogonal (perpendicular), then their dot product is 0. We use this to solve the…

Q: Suppose U and W are vectors in R" then ||U +W|| - ||U|| + || W|| if the angle between U&W is equal…

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Q: v, =,v, =, v, =

A: To add or subtract two vectors, add or subtract the corresponding components of each vector. For…

Q: Suppose that u and v are vectors in R7 both of length 2/2 and that the length of u- vis also2 /2.…

A: We can evaluate  the given problem as follows:

Q: u.v<0, u.w < 0 ,w .u < 0 ?

A: Given data:     The given first vector is: u. The given second vector is: v. The given third vector…

Q: In general, show that the vectors V = ai + bj and W = -bi +aj are always perpen-dicular. Assume a…

A: Given vectors are v=ai+bj and w=-bi+aj, where a≠0 ,b≠0. We know that two vectors are perpendicular…

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: Let the vector ü = (k,5,-1) and v=(2k,k,3) are perpendicular in R, find the value of k that related…

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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: Suppose that u and v are vectors in R7 both of length 2√2 and that the length of u - v is also²√².…

A: Solution :

Q: Suppose thatu and v are vectors in both of length and that the length of u-v is and the angle…

A: Let's find.

Q: If {v1, v2, . . . , vn} is a linearly dependent set of vectors, prove thatone of these vectors is a…

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Q: 5) Suppose that the set of vectors {ỉ, 7, w} is linearly independent. Prove that Span({ū, T}) #…

A: Given that u→,v→,w→ is linearly independent. Prove Spanu→,v→≠Spanu→,v→,w→.

Q: Show that if u and v are n-vectors, then u · v = uT v.

A: Consider the n vectors  u=u1u2u3.un,v=v1v2v3.vn

Q: If y is orthogonal to the vectors u and v, then y is orthogonal to u+ 3v. True False

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

A: Solve the given problem.

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

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Q: For any vectors u, v and w, show that uxv=uxw does not always imply v = w. Prove that u v ≤ ulv, and…

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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: 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: Suppose that u and v are vectors in R7 both of length 2 /2 and that the length of u - v is also2 /2.…

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Q: Suppose u, v, and w are vectors in R³ and W = span{u,v,w}. Let x be a vector in R³ that is…

A: We are given that x is orthogonal to each of the vectors u, v, and w. Thus, x is orthogonal to any…

Q: Suppose ~u and ~w are vectors in R^n . Prove that if ~u and ~w are parallel vectors in the same…

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Q: Prove that two vectors v = (a, b) and w = (c, d) are perpendicular if and only if ac + bd = 0

A: we have to prove that the two vectors v=a,b and w=c,d are perpendicular if and only if ac+bd=0

Q: If x, y are two no vectors, then prove that |xty | || X lle y llq by = + // use Holder inequality.

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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: For any vectors u, v in R', we havelu + ū|? = [u|2 + [ū]2 True False

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Q: 9. Show that for any real numbers a and b the vectors u = ai and v = bj are orthogonal?

A: Topic:-  vector algebra

Q: If u • vx w or v • or w • v equal to zero, then the vectors u, v , and w are coplanar... True False

A: Concept Used: Three vectors are said to coplanar if their scalar triple product is zero That is  [u→…

Q: Suppose that u, v and w are vectors such that (u, v) = 2, (v, w) = -3, (u, w) = 5, ||u|| = 1, ||v||…

A: Suppose that u,v and w are vectors such thatu,v=2,v,w=-3,u,w=5,u=1,v=2 and w=7Find the value of…

Q: When the set of vectors {u1, u2, . . . , un} is linearly independent and the set {u1, u2, . . . ,…

A: We have given; The set of vectors {u1, u2, . . . , un} is linearly independent and the set {u1, u2,…

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

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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: Consider the set of vectors {u" ,v ,w° } in R°, where u =(4,-4,8), v =(9,6,3) and w =(-9,-21,k),…

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Q: Suppose that u, v. and w are vectors such that (u, v) = 2, Evaluate the given expression. (v, w) = -…

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Q: If i • ( or v• (u x w) or w • (u x 7) equal to zero, then the 3, and w vectors u. are coplanar.…

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Q: Show that for any two vectors u and v: = |

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Q: b) Show that the vector w = u – proj,u is orthogonal to proj, u

A: The expression for the vector projection of u onto v is: projvu=v·uv2v Given: u=3,4,0 and v=-2,3,-6…

Q: If u, v, and w are vectors in R° , where u is non zero and u X v = u X w, then v = w. Select one:…

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