Let B = (1, x, x², x³) be an ordered basis for P3. Find the coordinate vector of f(x) = - 823 6x? – 9x + 3 relative to B. fB =

Q: 4 Let A = and define T : R? → R? by T(x) = Ax. Find a -2 -1 basis B such that the matrix [T]s is…

A:

Q: Find a basis for the kernel of the linear operator T(x, y) = (4x - y, -16x + 4y), Using the…

A:

Q: Let B be the basis of P, consisting of the Hermite polynomials 1, 2t, - 2+ 4t, and - 12t + 8t°; and…

A: Consider the Equation

Q: Let B = {1, x, x², x*} be an ordered basis for P3. Find the coordinate vector of f(x) = 4x3 – 72² +…

A: ANSWER:

Q: Let B = (1, x + 8, (x – 1)², 5x³) be an ordered basis for P3. Find the coordinate vector of %3D f(x)…

A: We have used the standard basis C {1,x,x^2,x^3} to write the coordinate vectors for f and each…

Q: 3 Find the coordinate vector of a with respect to the basis B for R3. 2 1.

A: We find the coordinate vector.

Q: Find a basis for R^4 that includes these two vectors.

A: Solution: Given vectors are: v0=0342,  v1=1121 We know that the standard basis of ℝ4 is e1,e2,e3,e4…

Q: Let B be the basis of P, consisting of the three Laguerre polynomials 1, 1-t, and 2- 4t +t, and let…

A:

Q: Let p = 5x + 10x + 3. Find the coordinate vector of p relative to the following basis for P2, P1 =…

A:

Q: Let B = {1+t, t – t2, 2t + t2} be a basis for P2. Find [-3+t – t°]B. %3D

A:

Q: Find the coordinate vector of p relative to the basis S = {p1, P2, P3 } for P2. p = 2 – 3x + 2x² ;…

A: Question from linear algebra.

Q: Find the coordinate vector of x2 + x - 17 relative to the basis {x² + 1, x + 2, x - 3}.

A:

Q: Find the coordinate vector [p(x)]B of p(x) = x² + 4x + 4 with respect to the basis B = {x³ + x – 2,…

A: According to the given information, it is required to find the coordinate vector.

Q: Let S = {v1, v2} be a basis of IR? where vi = and What element of R? is determined by the linear V2…

A:

Q: Y1 Y2 ER3 [Y3. (x, y) 2x1y1 + X2Y2+5x3Y3, for x = |X3 (a) Find a basis for the orthogonal complement…

A:

Q: Find the matrix A' for T relative to the basis B'. T: R2 - R2, T(x, y) = (x – y, y – 4x), B' = {(1,…

A: The given transformation is Tx,y=x-y,y-4x and the basis B'1,-2,0,3.

Q: 1) Interpolate (by hand) the data x = [-1,0,1] %3D y = [0,1,3] using a) the linear spline basis;

A:

Q: Find the matrix A' for T relative to the basis B'. T: R2 → R, T(x, y) = (4x – 3y, 5x), B' = {(-2,…

A: We have to find the matrix A' for T relative to the basis B'.

Q: Find a basis fo

A: Given,            A=3-916-26-161-38

Q: Let B be the basis of P3 consisting of the Hermite polynomials 1, 2t, - 2 + 4t“, and - 12t + 8t°;…

A:

Q: .

A:

Q: 3) Let S contain vectors of the form f(x) = a + bx + cx² + dx³ : f(-2) = 0 and f'(-4)= 0: Then a…

A:

Q: Let B be the basis of P2 consisting of the Laguerre polynomials 1, 1 -t, 2 – 4t + t2, and let p(t) =…

A: Let β=1,1-t,2-4t+t2 be the basis for P2R For Pt∈P2R , can be written as linear combination of…

Q: Find the coordinate vector of p(x) = 3 - x + 4x2 with respect to the basis B = {1, 1 + x, -1 + x2}…

A:

Q: Suppose T(v1) = w1 + w2 + W3 and T(v2) = w2 + w3 and T(v3) = W3. Find the matrix A for Tusing these…

A:

Q: Find the matrix A' for T relative to the basis B'. A' = T: R² R², T(x, y) = (x + y, 3y), B' = {(-4,…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Define T: R2→R? by T(x) = Ax, where A is the matrix defined below. Find a basis B for R? with the…

A: A=2-349 Characteristic equation of A is given by  λ2-trAλ+detA=0 , where trA, detA denote the trace…

Q: ind the matrix A' for T relative to the basis B'. T: R² → R², T(x, y) = (-2x + y, 2x - y), B' = {(1,…

A: We have to find matrix

Q: Find the coordinate vector of p(x) in P., relative to the basis S= {p,.P.-P;}, where p(x) =…

A:

Q: What is the coordinate vector for the polynomial p(x) = 2 – x² + x'relative to the standard basis…

A: our objective is to find the coordinate vector for the polynomial p(x).

Q: Find a basis for the kernel of the linear operator T(x, y) = (6x - y, -24x + 4y), Using the…

A: It is given that the linear operator Tx,y=6x-y,-24x+4y. Find the kernel of the linear operator.…

Q: The set C = {1+ t²,t +t², 1+ 2t + t²} is a basis of P2. Find a vector q e P2 such that [q]c

A:

Q: Find the matrix A′ for T relative to the basis B′.T: R2→R2, T(x, y) = (−3x + y, 3x − y), B′ = {(1,…

A:

Q: Find a basis for the kernel of the linear operator: T(x, y) = (5x – y, −20x + 4y) NOTE: Using the…

A:

Q: Let P2 denote the vector space of all polynomials in the variable a of degree less than or equal to…

A:

Q: Let B be the basis of P, consisting of the Hermite polynomials 1, 2t, -2+ 4t2, and - 12t + 81°, and…

A:

Q: Find the coordinate vector of = -1 with respect to the basis B = for IR3. 2 B

A:

Q: Find the coordinate vector of a -2 with respect to the basis B %3D for R.

A:

Q: Find the coordinate vector of Prelative to the basis S = {P,P2P3} P1 = 1+ x + x, P2 = x + x²,P3 =…

A: Vector

Q: Find the coordinate vector of p(x) = 5 - 2x + 4x² with respect to the basis B = (1 + x, 1 – X, x?}…

A:

Q: .2 The set B= {1 +t,-t-t,1+2t+t} is a basis for P,. Find the coordinate vector of p(t)= -3-5t-6t…

A:

Q: 2) Find the coordinate vector [x]p of x relative to the basis B={b1, b2}: [-3] bị = G.b2 = x =G

A:

Q: Explain why S is not a basis for P,. S = {1 – x, 1 – x², -1 – 6x + 7x2} || O sis linearly dependent.…

A:

Q: Let B (1, x + 3, (x – 1)², 5æ³ ) be an ordered basis for P3. Find the coordinate vector of f(x) =…

A:

Q: Explain why S is not a basis for P. S = {1, 2x, =7 + x², 9x} O S is linearly dependent.

A:

Q: 3 Find the coordinate vector of x = -2 with respect to the basis B for R3. -2 6 ||

A: Given that the vector x→=3-2-2 and the basis is 166,01-5,001. It is required to find the coordinate…

Q: Explain why S is not a basis for P2. S = {1 – x, 1 – x², -1 – 6x + 7x²} O sis linearly dependent.

A: Given that S=1-x,1-x2,-1-6x+7x2 Explain why S is not a basis for P2 if S is linearly dependent the S…

Q: Let B = (1, x + 2, (* – 1)", 9x) be an ordered basis for Pg. Find the coordinate vector of f(æ) = 8a…

A: Answer

Q: Explain why S is not a basis for P,. S = {1 – x, 1 – x2, -1 – 7x + 8x²} O sis linearly dependent. O…

A:

Q: Let B be the basis of P, consisting of the three Laguerre polynomials 1, 1-t, and 2- 4t + t, and let…

A: Find your answer below

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.