Let B be the BaJil OF Rd Consdting of lectory 9nd kt c bc the basis consisHing of 2. Find q sA tnX P lach thet [x]< = PCXIR * For all X ih R

Q: Recall that P, is the collection of all polynomials of degree 2 or lower. Let S be the collection of…

A: Given that S=-3t2+t, t2-3t-4 (a) The linear combination of these vectors is,…

Q: Let z= y- 4a, a u'v and y-v- 3u. Compute On kum)-(1,1) -

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Q: Find a basis of ker T. T: M22 → 1 M22; T( x ) = AX, where A = 0 0 O[1 0 0 1 0 1 1 0 1 0 1 0 0 -1 0…

A: The transformation T:M22→M22; T(x)=AX, where A=1100. We have to find the basis of kerT.

Q: Let β = { u1, u2, .. . , un} be a subset of Fn containing n distinct vectors, and let B be the…

A: Given that, β=u1,u2,...,un is a subset of Fn and let…

Q: 59. In R4, given 2 nullspaces 1 2 00 1 V : |-1 0 -1 m 0- Find m such that dim(U n V) is max. Find…

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Q: 2. Define the map T:P2¬P4 by T(f) (x)=f(x²), Please determine the rank of I by using standard basis.

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Q: b. S = {1+t,1– t,t – t²} in P2 using the inner product (p(t), q(t)) = | p(t)q(t)dt (P2 is the set of…

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Q: (c) Let V and W be given as above. By using linear extension method, determine whether V is…

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Q: Find the coordinates in R° of x = (13, 26, 39) relative to the orthonormal basis 12 5 12 B = 13 13…

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Q: Let ẞ= {v1, ••• , vn} be an orthonormal basis for Rn. (a) Prove that, for any x and y in Rn, x · y =…

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Q: Let A E Mnxn(R), show that it is possible to express A as the product, A = PQ where P,Q € Mnxn(R),…

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Q: Is this the basis? What is the rank of A?

A: According to the given information, it is required to find the basis and rank of matrix A. The…

Q: Let P3[t] denote the vector space of all polynomials in t of degree at most 3 with real…

A: To show that the given set is a basis for P3[t], it is sufficient to show that any element in P3[t]…

Q: If A is an nxnmatrix with det(A)÷0, then A has a QR- decomposition. Select one: O True O False

A: The given statement is True. Given that A is n×n matrix with det(A)≠0 this implies that rank of…

Q: (2 3) Let A = Verify the Cayley-Hamilton theorem. Use the theorem to express 1 2 A² and A3 as linear…

A: The given matrix is A=2312. Cayley-Hamilton theorem: Cayley-Hamilton theorem states that, "Every…

Q: Derive formulation for the elements of c(m, m') modified Daniell Kernel

A: Given information: The information about modified Daniell kernel is given.

Q: Let QE M,(R) be given such that the columns of Q form an orthonormal basis for R". Prove that Q'Q =…

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Q: Find the degree and a basis of the extension field Q(v3, v7) Q(V3 + v7). over

A: This question is from field theory's topic extension of field. Solution is given below.

Q: (b) Find the orthogonal decomposition of v with respect to W. projw(v): %3D perpw(v)

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Q: Let B= { }].[),A} be basis for IR Is B orthonormal ? O False O True

A: Applying orthonormal property we have

Q: Consider the linear operator L: BC[0, ] → BC[0, 7] defined by Си — и" - 2и is unbounded in the sup…

A: Consider the linear operator L:BC0,π→BC0,π defined by: Lu=u''-2u. We know that the set BC0,π is…

Q: Let A E Mpxn(F), and let B be the set of rows of A. Prove that B is a basis of F" if and only if…

A: The proof of given question is solved below.

Q: Find a basis {p (x), q (x)} for the vector space {f(x) = P3[x] | ƒ' (−1) = ƒ (1)} where P3[x] is the…

A: We have to find p(x) and q(x).

Q: Find a basis for the solution space. (If a basis does not exist, enter DNE into any cell.) X1 - x2 +…

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Q: Let A be a diagonalizable 3x3 mat rix with P-AP=-I , where I is the identity mat rix. Which of the…

A: given that A is a diagonalisable 3×3 matrix such that P-1AP=-I where I is the identity matrix .

Q: 300311 By reducing to reduced echelon form, find a basis B of the null space, N(A) of A = 31151…

A: The given matrix is A=30031311510224003361. Find the basis B for the null space of A as follows.…

Q: (a) Prove that the set ẞ = {p0(x), p1 (x), ... , Pn(x)} of Lagrange polynomials is linearly…

A: Given: ẞ = {p0(x), p1 (x), ... , Pn(x)} To Prove" (a). Prove that the set ẞ of Lagrange polynomials…

Q: Show that B = {1+ 2t, t – t2,t+t2} is a basis for P3. ) Let p(t) = 1+3t +t. Compute [p(t)]s- (a) (b)

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: 21: Let L: M22 → M22be defined by L(A): =E [1 2j [3 4,for AinM22. Consider the ordered basis or M22.…

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Q: 3. Define a mapping T: P3-P3 by. T(f(x))=f(x) Please find the nullity of T. (Hint: Still dx by using…

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Q: 5. Let T: IR'Ie bé the livear trainstormation de fined by T(X,X]<(xi+3Xz,?x;-S X2). and B= {u, Uz}…

A: A linear transformation is a function from one vector space to another that respects the underlying…

Q: Let A be a diagonalizable 3x3 mat rix with PAP=-I , where I is the identity mat rix. Which of the…

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Q: Let 8 be the basis of På consisting of the Hermite polynomials 1, 2t, -2+ 41 and 12t+Sttand let p…

A: Suppose V is a finite dimensional  vector space over field and is a basis. Then, every element of…

Q: Consider P2, endowed with the following inner product: 1 1 (p, q) : G P(0)q(0) + G P(1)q(1) + for…

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Q: let f Cox) = 4 glx)=-9x+7 %3D Consider the 1aner preduct t the vector s pece P of polymonmials Ure…

A: Given that fx=4gx=−9x+7hx=−4x2−8x−2 To use Gram–Schmidt process to determine an orthonormal basis…

Q: onsi with its standard product. nat A E Mnxn(R) is orthogonal if and only if, for any orthonormal…

A: since {v1,...,vn} is orthonormal , thenvit * vj=0 if i different than j and 1 if i=j where I wrote…

Q: Let β ={x1,...,xn} be a subset of Fn containing n distinct vectors, and let B denote the element of…

A: Assume that β ={x1,...,xn}  is a basis for Fn.Let B denote the element of Mnxn (F) whose jth column…

Q: Let T be the linear thansformation from R5 to Rª defined by X1 1] X2 X1 1 3 2 X2 -8 1 -2 2 0 -1 4 X3…

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Q: Find the basis and dimension of the kernel and the image of G, where G(x, y, z, s,t) = (x + 2y + 2z…

A: First, we find the matrix corresponding to this transformation. Then apply row reduction to that…

Q: 6.2 De fine T: P, →P. bj T Cp) = P! klhat is the kernel of T? (Use 9o, 9, 9, - - - as ar bi trary…

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Q: Given a basis B = {V1, V2,, Vn} of Subspace S, there is a unique way to express any ... vE S as a s…

A: We will first write 2 expressions of v as a linear combination of basis vectors in B. Then, we will…

Q: Show that the set S = {p1.P2-P3} is a basis for P2 (space of polynomials of degree less or equal to…

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Q: Let K„(x) = ane¯nl2l, x E [-T, T]. Prove that there are constants a, for which the K, form a family…

A: Given  Knx=ane-nx , x∈-π,π Let Kn form a family of good kernels. Then…

Q: , Find a basis {p(x), q(x)} for the vector space { f(x) e P3[x] | f'(-5) = f(1)} where P3[x] is the…

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Q: 1.2 Find a basis B for the domain of I Suh that the mahix for ī alative to Bis iagend. Hogand. T:…

A: We have to Find a basis B for the domain of T such that the matrix for T relative to B is diagonal.

Q: Consider the following. V = P2, B = {1, 1 + 5x + 6x?} Complete the following statements. The…

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Q: 60. In R4, given a nullspace V = {(x1; X2; X3; X4) E R4|¤1 – *2+ x3 = 0 A x2 + x3 + x4 = 0}. %3D…

A: see below the answer and explanation

Q: 14. Consider the basis * B = {1+ x + x², x + x², x²}. for P2. Let p(x) = 2 + 3x + 2x². Then [p(x)]B…

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Q: Let T: P2 that is, 7. > P2 be the linear operator T(p(x)) = p(2x+ 1), T(co+ C,x+ C,x²) = c, + c,(2x…

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Q: 6. Determine the basis for the null space of: -2x +2y + 2z] Зх + 5у + z 2у +z a) х — 2у — z b) —х +…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.