a. Is W = {ann + an-1xn-1 + •+aix+ao anan-1a₁a0 = 0} a vector space with the same operations in R[x]? b. Is W = R² where (a, b) (c,d) = (a + b), c+d) and a (a, b) = (aa, ab) a vector space? c. Is W = {A € Mn,n (R|A = AT} ≤ Mn.n(R)?

Q: 2. Let P2(R) be the vector space of polynomials over R up to degree 2. Consider B = {1+x= 2x°, -1+a…

A: given B=1+x-2x2 , -1+x+x2 , 1-x+x2B'=1-3x+x2, 1-3x-2x2 , 1-2x+3x2 b) find the coordination matrices…

Q: If V is a vector space then show that cV=V.

A: Vector space: A non-empty set V closed with two binary operations called addition and scalar…

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Q: 6. (a) Let u, v, w be three linearly independent vectors in Euclidean Space R^7. Determine a value…

A: we have to find the value of for the linearly dependent and linearly independent

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Q: Please explain why  If V� is a vector space and u� and v� are vectors in V�, then according to the…

A: V is a vector space and u and v are vectors in V.

Q: 7. Given that a,b and are three vectors whereas is a scalar such that axř=b+ã and a = 2. By using…

A: Vector triple product is used

Q: 2. Determine whether the following sets with the corresponding vector addi- tion and scalar…

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Q: What is the dimension of the vector space S=abc detEM2x3(R): a=b=c=0}

A: Dimension of vector space is number of element in basis

Q: Question 35 Let B = {b1, b2} and C = {C1, c2} be two bases for a vector space V. You are given that…

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Q: Given the vector (x <- c(5, 2, 7), what would x^2 return? O [1] 78 O [1] 196 O [1] 25 4 49 O [1] 10…

A: Given that, the vector is        ,we need to find .

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: r- {{: :] T = " E M22| a = - dis a vector space under standard matrix addition and scalar…

A: I have proved T is a subspace

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Q: vector

A: (a+b)(v+w) = (a+b)v + (a+b)w

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Q: 1 Defined in P,(R), p(x)=1,q(x)=x- and h(x) =x² -: -x+- 6. Investigate whether the vectors are…

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Q: If {v1, V2, V3} is an orthogonal set of nonzero vectors in an inner product space V, then prov that…

A: This question is related to linear algebra (inner product space).

Q: A C -³/4 - 1/4 9/8 - 1/4 - 1/4 AZ = O 1/8 1/4 Find the vector 7 such that. 2 O (note: DON'T USE…

A: Give that, A-1=-34-14098-1814-14-140 and Ax→=206 We have to find the value of x→

Q: Show that there do not exist scalars c₁, c₂, and C3 such that c₁(1,0, 1,0) + c2 (1, 0, 2, 1) +…

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Q: Question 35 Let B = {b1, b2} and C = {C1, c2} be two bases for a vector space V. You are given that…

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Q: Suppose V={v1,v2,...,vn} is a set of nonzero vectors, and let                    x= a1v1 + a2v2…

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Q: d). Let K = {(x;y) | x,y e R} with operations (x1;y1) (X2;y2) = (x, + x2 + 1; y, +y2 - 2) %3! (ax, +…

A: Given: K=x;y | x, y∈ℝ with operations x1, y1⊕x2, y2=x1+x2+1; y1+y2-2 and a⊗x1;y1=ax1+a-1; ay1-2a+2.…

Q: 4. Let V = R³ and let T: V →V be the linear map given by T(r, y, 2) = (2x + z, y – x+ 2, 32) (you do…

A: