Given a vector s (v₁),e m, and let where |J|= n. T uch that LnI= e same subspace

Q: What is the dimension of the subspace H of R spanned by the given ved V1, V2 and v3 2 3 Vị = -8 V2 =…

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Q: = f(x,y) = e²+y. For a unit vector u in R?, it is fü(0, 0) = 1. Let z true that

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Q: find the given vector  Unit vector ew where w = (24, 7)

A: Given: w=24,7

Q: If u is a unit vector and a is a positive scalar satisfying au + = 0, find a and u.

A: Given: u is a unit vector and the scalar a is positive satisfying the equation au+1,-2,5=0 To find…

Q: Find the vector with the given length || v || = 3, and in the direction of u = (0,2,1, -1)

A: Sol

Q: A vector y in Rn can also be viewed as an n × 1matrix Y = (y). Show that ||Y||2 = ||y||2

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Q: If å = v2i +j - k, what is the vector whose alignment a is in the opposite direction and its size…

A: Given a→=2i+j−k We have to find the vector whose alignment a→ is in the opposite direction and its…

Q: Prove that Ov = 0 for any vector ve V. Make sure to justify all your steps!

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Q: The curd of the vector funchion v = Jx i+ Jgj+ ZK is ☺ xi+ yj+ zK

A: It is given that, v→=x i^+y j^+z k^   According to curl, the swirl of a vector around a point. It is…

Q: Find c so that the vector v is orthogonal to W = ||

A: Given: v=1c. w=2-1 Vector v and w are orthogonal only if the dot product of vectors is zero.

Q: Find a vector v parallel to u=4i−3k and with magnitude ||v||=4

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Q: Let j = | and ü .Write j as the sum of two orthogonal vectors, it -2. %3D an {u} and ¤2 orthogonal…

A: Given:- →y=-69  →u=5-2

Q: find the components of the vector −→P Q. P = (1, 0, 1), Q = (2, 1, 0)

A: Given  P=<1,0,1>Q=<2,1,0> The component form of a vector is the ordered pair that…

Q: 6. Find the following. a. Find the B-coordinate vector of s(t) = 4+5 sin?(t) given B = {1, sin(t),…

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Q: -3 6. Let u = 0 |and i =| 1 Find a vector ü not in span {u, v}. 1

A: A vector w→ does not lie in the span of the vectors u→,v→ if determinant of the matrix formed by…

Q: 33. Define T: R³ → R³ by y + 2z 2x +3y - z x +2y - 2z x - y a. Find all vectors in R' that are…

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Q: Find an initial point P of a nonzero vector m = P& with terminal point O(3. 0. -5) and such that (a)…

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Q: Find a vector function that represents the plane that passes through thepoint p0 with position…

A: The plane passes through the point p0 whose position vector is r0→. The plane also passes through…

Q: Let a,b be scalars. Find a vector perpendicular u=

A: Given u = <a,b>                   a,b are scalarlet v be the vector perpendicular to uv =…

Q: Consider the vectors v1, v2, ..., Um in R". Is span (01,..., īm) necessarily a subspace of R" ?…

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Q: Let x = (2, 5, 1) and y = (−1, 3, 2) be two vectors in R3. Compute xTy. Compute xyT. Are x and y…

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Q: For what value of c is the vector v = ⟨2, -5, c⟩ orthogonal to w = ⟨3, 2, 9⟩?

A: Two vectors are said to be orthogonal if their dot product is zero.

Q: Sample Problem 1.9 Given the vectors A = 8i + 4j - 2k N B = 2j + 6k m C = 3i - 2j+ 4k m calculate…

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Q: Let u = (-1,0,1), v= (3,2, 1) and w = (0,1, 2) . (a) Prove that the vectors u – v, u+ v and u x v…

A: Given : u=<-1,0,1> v=<3,2,1> w=<0,1,2>

Q: (x, y, z) = ( i i

A: Given that Length of vector = 6√3 We have to find component of vector.

Q: Let ū = (3,2), v = (-2, –2), and w = (-4,3). Find the vector x that satisfies 5u – v +x = 7x + w. |…

A: Given that u→=3,2v→=-2,-2w⇀=-4,3