Let U=span(ū, ,ū,,ū and Û=span {u, ,u,, where ü,=(1,0,0,0), ū,=(0,1,1,0), ủ,=(0,1,1,1) and ů,=(1,0,0,1), ủ,=(1,1,0,0), ủ=(0,0,1,1). Show that U & Û are vector spaces (over the field R).

Q: Let u = (9,3,-3), v = (0,2,-5), and w = (6,5,4). Compute v X w. vxW=(

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Q: Let u = (2, 3, 1), v = (1, 3, 0), and w = (2, -3, 3). Since (1/2)u -(2/3)v - (1/6)w = (0, 0, 0), can…

A: A set of vectors u1, u2, ……, un is said to be linearly independent if c1u1+c2u2+……+cnun=0 implies…

Q: Theorem 23. If u, v E Q then we can find integers a, b, d with d > 0 such that u = a and v = d'…

A: By Division Algorithm we know that,               Let a, b be two integers with b>0. Then there…

Q: Find u, u = (-1, 4), v = (4, 5) (a) ||u|| v, uv, and d(u, v). (b) ||v|| (c) (d) U V d(u, v)

A: The given vectors u=-1, 4, v=4, 5. We have to find the values of u, v, u.v, du, v.

Q: V₁ = M 0 , V₂ = 1 and V3 = 11 0 -5 [3] เย เย Use the Gram-Schmidt procedure to produce an orthogonal…

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Q: 3. If A = {1, 2} and B = {x, y}, then AXB = O {1,x), (1,y), (2,x), (2,y)} O {1,x), (2.y)} none of…

A: We have to solve given problem:

Q: Determine whether each statement is true or false   (a) A ∩ A'= φ (b) If A ⊆ B, then A ∩ B = B.…

A: Explanation of the solution is given below...

Q: 3) u = y f( ise XU, + yu, t zu. = ?

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Q: If v = (2, 2, 0) and w = (-1,4, 0) , what is v × w ? (10, 0, 0) о (), 0, 6) (0, 0, 10) о (10,0, 6) О…

A: Apply formula for vector cross product

Q: Find the transitive closure of R={(0,1),(0,2),(1,1), (1,3),(2,2),(3,0)}

A: Given relation is                              R=(0, 1), (0, 2), (1, 1), (1, 3), (2, 2), (3, 0) we…

Q: In Exercise 22, let u = PQ\ and v = PR\ , and find (a) the component forms of u and v, (b) u ∙ v,…

A: a) Answer(a): u=(-2,6,-2) and v=(3,6,-3)

Q: Assume that U= { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }, A = { 2, 5, 7, 8 } and B = { 1, 4, 5, 7 }. Find…

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Q: AP'Q'R' Is a translation of APQR. Write the translation rule. 10f R' 8.

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Q: Given F(A, B, C, D) = A'B'C'D' + A'B'C'D + A'BCD' + A'BCD, express F(A,B,C,D) and F '(A,B,C,D) in…

A: Solution: Given that F(A, B, C, D) = A'B'C'D' + A'B'C'D + A'BCD' + A'BCD Now, truth table Row no.…

Q: Does S={(1,0,1),(2,1,0),(3,,1,1),(1,1,1)} spans R³ ? Select one: O True O False

A: Given: S={(1,0,1),(2,1,0),(3,1,1),(1,1,1)}

Q: Compute Cov(X,Y)

A: Solution: From the given information, the joint distribution is

Q: Let W(s,t) F(u(s, t), v(s, t)) where u(1,0)-4, u,(1,0) 3, u(1,0)- 5 v(1,0) 7, v.(1,0)=-3, v(1,0)--6…

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Q: Let W1=span{(1,1,0),(-1,1,0)} and W2=span{(1,0,2),(-1,0,4)} Proove W1+W2=R^3

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Q: If U = {0,1,2,3,4,5,6,7,8,9}, find (U∪∅)'

A: Given that  If U = {0,1,2,3,4,5,6,7,8,9}, find (U∪∅)'

Q: if u = <1,-3,1> and v = <2,2,2> then find the projection of u onto v

A: The objective of this question is to find the projection of vector u onto vector v. The projection…

Q: If u=(1,4)�=(1,4)  and v=(3,2)�=(3,2)  then proju(v)≈

A: The objective of this question is to find the projection of vector v onto vector u. The projection…

Q: 5- Suppose that A = {x1 = (3,1,2), x2 = (0,0,2), x3 = (2,0,1)} then [A] = R³, that means for every…

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Q: Let U= {1, 7, 2, 12, 5, 10, 20, 18} A = {1, 20, 18} C = {7, 2, 12, 5, 10} Find A U C'.

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Q: 2. Assume u = Z, and let A B = {..., -6, -4, -2,0,2, 4, 6,...} {-9, -6, -3,0, 3, 6, 9,...} {...,…

A: According to guidelines we can solve only first three subparts and rest part can be reposted…

Q: Suppose that f(2, 3,1) = 5, fz(2,3,1) = 2, fy(2,3,1) = 3 and f.(2, 3,1) = -1. %3D Then f(1.9, 3.3,…

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Q: A = (a, b, c, d] X= [1, 2, 3, 4} Select the definition for f that is a well-defined function. O 1) f…

A: Let, A and X be two non empty sets. A function f: A -----> B is an assignment in which each…

Q: If (X,7,) and (X,7,) T. - spaces, then (X,7,nt) is also a T,- space. GOOD LUCK

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Q: 5. For which value of x do the following vectors form a linearly dependent set in ¹ X₂ G

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Q: Let W(s, t) = F(u(s, t), v(s, t)) where u(1,0) = -2, u, (1, 0) = 8, ut(1,0) = -4 v(1,0) = -3, v.…

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Q: determine whether (1, -3, -3) belongs to the span of {(1, -1, 1), (1, 1, -1), (-2, 2, -2)}

A: write all 3 vectors in the matrix A=11-2-1121-1-2 the vector b is b=1-3-3 if the system Ax=b is…

Q: 22. Let v₁ = (1, 6, 4), v₂ = (2, 4, -1), V3 = (-1, 2, 5), and W₁ = (1, -2,-5), w₂= (0, 8, 9). Use…

A: Given vectors are Here observed that So we have each of .In other words ,

Q: 0-2.5) R= (9, 4) P= (3, 2) Q= (7, 2) S-(10, 2) N= (0. 0) -1 10 11 -1 T= (-1, -2) L=(4, 2) U= (0, -2)…

A: Shape of triangles KLM, NOP are same and triangles TUV, QRS are same. But to prove congruent nature…