Let V = (a, b, c, d), such that a = 2b − c, b = 2d − 3c, and d = a − b + c. Find the dimension of V .

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Q: Find a and b such that v = au + bw, where u = (1, 2) and w = (1, -1). v = {8, 1) a = b =

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Q: B = { t,f,-3 is compact. IS %3D

A: See the attachment

Q: be the bases of V, W and U respectively. If t: V→ W, s : W→U are linear transfor-

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Q: Let a = ci + jand b = 9i + 36j. Find c so that a and b are orthogonal. %3D

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Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, –1). %3D %3D = (0, 6) V = a b…

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Q: Given K= (-2,-1), L=(2,4), M= (-3,-1) and N= (1,4), Prove that KĽ and MN are equivalent by Showing…

A: Two vectors are Equivalent if they have same magnitude and direction.

Q: Let a = ci + j and b = 3i + 3j. Find c so that a and b are orthogonal. %3D C = i

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Q: Let v (k,2k,1) and w (k,-1,-8). For which values of k are v andw orthogonal?

A: Calculation:Since it is given that v and w are orthogonal, v ∙ w = 0.

Q: Given: G is the centroid of AAEC, EB I AC, AB = 6, AF = 5, EG = 5÷, %3D and AE = CE. EB = E. А 2 В 8…

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Q: Find a and b such that v = au + bw, where u = ⟨1, 2⟩ and w = ⟨1, −1⟩. v = ⟨1, −3⟩

A: Given: v=au+bw; u=1,2,v=1,-3,w=1,-1 for finding value of a and b, we put value of u,v,w in given…

Q: Find a and b such that v = au + bw, where u = ⟨1, 2⟩ and w = ⟨1, −1⟩. v = ⟨−1, 8⟩

A: Given that v = au + bw. Substitute u =<1, 2> and w= <1, -1> in v.…

Q: a) Prove that ||u + v|| = ||u - v|| if and only if u and v are orthogonal, (b) Draw a diagram…

A: a) Suppose u,v are orthogonal. Now…

Q: The norm of the set {cosh(i nn x},n E N, –-2<x<2 in the Hermitian sense is:

A: Given,                  cosi nπx, n∈ ℕ, -2≤x≤2

Q: Show that if v and w lie in the yz-plane, then v × w is a multipleof i.

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Q: Find a and b such that v = au + bw, where u = ⟨1, 2⟩ and w = ⟨1, −1⟩. v = ⟨4, 5⟩

A: we have to find a and b such that v=au+bw where u=1,2 and w=1,-1 and v=4,5. the given vectors are:…

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Q: Find the norm of i and the unit vector i in the direction of a if ||7|| =

A: Solutions

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Q: 11. Let a, =3 ,b3-5 For what value(s) of h is b in the plane spanned by a, and a2?

A: We have to find the value of h

Q: Find the area of the parallelogram spanned by v = (1, 1, 1) and w = (0, 0, 2).

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Q: Let u = (k, 2 − k, −1), v = (2k, k, 3). Find k such that u and v are orthogonal.

A: Let u = (k, 2 − k, −1), v = (2k, k, 3)

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A: Projection vector of a⇀ on the b→ is given by c→=a→·b→b→b^

Q: Let a=ci+j and b=3i+6j. Find c so that a and b are orthogonal.

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Q: If A %3D аx + За, and B %3D 5ax + 2а, — баz, find @AB- АВ

A: ANGLE BETWEEN TWO VECTOR

Q: Let T={(a, 0): aER}, then T is Borel algebra.

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Q: If the column space of A is C(A) = R", then det A +0. %3D O a. TRUE O b. FALSE

A: The solution are next step

Q: What is the Cartesian Product of Z × X × Y, where X = {3,–1}, Y = {m, l, 0} and Z {w,b}.

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Q: Find the norm of v, and a unit vector that is oppositely directed to v. (a) v = (3, 3)

A: The given vector is v = 3, 3

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Q: Find a and b such that v = au + bw, where u = ⟨1, 2⟩ and w = ⟨1, −1⟩. v = ⟨−6, 0⟩

A: It is given that,  v = au + bw, where u = ⟨1, 2⟩ and w = ⟨1, −1⟩. v = ⟨−6, 0⟩

Q: Is it true that if x is orthogonal to v and w, then x is also orthogonal to v − w?

A: x is orthogonal to v and w. Then their dot product is zero. That is, ⇒x·v=0  &amp;  x·w=0

Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, –1). v= (0, 24) a = %3D

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Q: Suppose that u, v, and w are vectors in an inner product space such that (u, v) = 1, (u, w) = 6, (v,…

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Q: ind the norm of x and the unit vector u in the direction of a if -5 * = ||| = %3D 2 2

A: The norm of a vector A→=abc is defined by A→=a2+b2+c2.

Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, -1). %3D v= (0, 6) %3D b =

A: Explanation of the answer is as follows

Q: Given: G is the centroid of AAEC, EBL AC, AB= 6, AF = 5, EG = 5, and AE = CE. EB B

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Q: Prove that Srxdr = 2[, , da, r × dr =

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Q: For what values of aare u and v orthogonal?

A: Consider the given vectors  u=11-2  and  v=a-12 Write the vectors in row form u=1,1,-2  and…

Q: Suppose that A = SS−1, where  is a diagonalmatrix with diagonal elements λ1, λ2, . . . , λn. Show…

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