Let Uz?la :a,bE R and :c;d eR be two Subspaces of M, CR). Show that U eW= M, IR).

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: 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: Let y = Lal: Let L be the line spanned by u. and u %3D Write y as the sum of two orthogonal vectors,…

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Q: Find the area of the triangle determined by the points P, Q, and R. Use * .the cross product of…

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Q: calculate v × w.v = v = (1, 1, 0), w = (0, 1, 1)

A: Given v=<1,1,0> and w=<0,1,1> v×w=i→j→k→110011         =i→(1-0)-j→(1-0)+k→(1-0)…

Q: Calculate the component of v = 〈− 2, 1/2 , 3〉along w =〈1, 2, 2〉.

A: Given: Vector, v=-2,12,3 Vector, w=1,2,2

Q: {(1, 2, 3),(3, 2, 1),(0, 0, 1)}. Show that B is linearly independent and spans R3.

A: Linear span: Let V represent a vector space, and S=(v1,v2,...,vn) represent a subset of V. If every…

Q: Let ū = (4, –2), ū = (-2,0), and w = (2, 2). Find the vector x that satisfies Tu – u +x = 5x + w. In…

A: Given Let Plugging the values in the equation:

Q: Let y = and u = Let L be the line spanned by u. Write y as the sum of two orthogonal vectors, YL in…

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Q: What is the dimension of the vector space ab c S= { EM2x (R): a =b=c} de f

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Q: Two linearly independent vectors in R3 span R2, is that true

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Q: 2s Let H be the set of all vectors of the form Find a vector v in R' such that H span {i}. -s S

A: Spanning set of H

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

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

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Q: Let S be the parallelogram determined by the vectors b₁ = The area of the image of S under the…

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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: Let a = (a1, a2), b = (b₁,b2) be vectors in R². The area(a, b) is given by 1b₂-a2b₁. (a.) Show that…

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Q: Show that if V is a real vector space and av=0, then a=0 or v=0

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Q: Let L be the line in R that consists of all scalar multiples of the vector 2 Find the orthogonal…

A: Concept:

Q: Let a and b be vectors in R?. (a.) Derive the area(2b + 5a, b – 2a) in terms of area(a, b). Explain…

A: Given: a,b∈ℝ2 If a=a1,a2 and b=b1,b2 then areaa,b=a1b2-a2b1. To do: Express the area2b+5a,b-2a in…

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: Let u = (2, -3, 4) and v = (-2, 1,3). What is the projection of u onto v (proj v u) and the scalar…

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