— 2х1 — 5х2 + 8хз x1+3x2 – 5x3 +x4 |3x1 + 11х2 — 19хз + 7x4 X +7x2 — 13хз + 5х4 x1 X2 . Let T X3 X4 a) Is T a one to one linear function? b) Does T map R* onto R4? ||

Q: Show that the function u(z, t) : satisfies ua = %3D %3D a2t2-2

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Q: Suppose that T : R2 --> R2 is linear, T(1,0) = (1, 4), and T(1, 1) = (2, 5). What is T(2, 3)? Is…

A:

Q: Express ax? + bx + c as a linear combination of the functions f(x) = 4, g(x) 2x, and h(x) = -x²,…

A: Sincewe can write every element of P2 in linear combination of f(x),g(x),h(x) so this functions…

Q: Determine whether the set {P₁, P2, P3} is linearly independent in P₂=1+2x+3x² + 4x³ and p3 P₂, where…

A: The solution follows as:

Q: b. In Z6(x], let f = 2 + x + 4x² + 3x³ and g = 4 + 3x+ 5x² + 3x³. Compute f + g and f.g and their…

A: In the finite field we only use the coefficients from that field . The degree of polynomial is not…

Q: Show that f(z)dr: S(#2-2) +4f(r2i-1) + f(#2)]- an"(c.)} m-1 h4 (0) +2f(2) + 4f(*2-1) + f(*) I80(6 -…

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Q: Show that the functions f, (x) = 4x" , and f2(x) = x"** are linearly independent on (-00, 00).

A:

Q: Suppose that 7(t) is a vector-valued function. Prove that (7 · (7'x7")) = (T'x ") dt

A: We will proof the required result.

Q: Let f (x, z) = 4xz³ – 2x + and g(x, z) = 3x – z+ 2xz –6. - Find: af(x,z) blank 1: evaluated at: x=3…

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Q: Show that the set {1, x, x2, ... , xn} is linearly independent in Pn(F).

A: Given, {1, x, x2, ... , xn}

Q: Prove that δ: M2×2(F)→F is a 2-linear function if and only if it has the form δ(A) = A11A22a+…

A: Consider a matrix of order 2 as,

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A: Here, to check the elements of P2 are linearly independent or not. For that, let…

Q: 4) B. Let A = {u, v, w}, B = {x, y, z}. Determine whether the relation R = {(u, x), (v, z), (w, y)}…

A:

Q: Prove that there is an additive function T : R --> R that is not linear.

A: Let T: V→W  be the linear transformation and we it is linear,…

Q: Use Fourier-Motzkin elimination to give a linear combination of the following in- equalities that…

A:

Q: Enter the function In standard form. y = 2(x-1)(x +5) The standard fom of y = 2(x-1)(x +5) is

A: y=2(x-1)(x+5) first multiply (x-1)(x+5) =>(x-1)(x+5) =>(x^2 +5x -x -5) =>(x^2 +4x-5)

Q: Let T : R → R³ be defined by: X1 T [3x1 – 12 – 5x12x17+ x2] X2 (a) Show that T is a linear…

A:

Q: Prove that f : R – {3} → R – {1}, defined by f(x) = is a bijection. x-1 x-3

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Q: Let f(x) = 3x² and. P = {–2, –1, 0, 1, 2, 3}. Compute Lf(P) and U,(P). %3D %3D

A: Consider: fx=3x2 and P=-2,-1,0,1,2,3. Compute LfP and UfP.   If P is a partition such that…

Q: Suppose that a linear transförmation / satisfies T(u,) = T(u,) = -1 -2 Find T(4u, - 3u,). T(4u, -…

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Q: 2.2: Determine whether the following polynomials u, v and w in P(t) are linearly dependent or…

A:

Q: Let T: R2 R2 be a linear trasformation such that T (x1, 22) T (x) = (3, 1). (x1 +x2, 2x1 + 3x2).…

A:

Q: Determine whether the set {P1, P2, P3} is linearly independent in P2, where p₁ = 2+x+3x² + 4x³, p₂ =…

A: Let V be a vector space . let v1,v2.....vn ∈V are linearly independent iff c1a1+c2a2+...+cnan=0…

Q: Exercise 3. Show that f : Z → N so that f (z) = z² + 1 for all z E Z is neither one-to-one %3D nor…

A: One-One Function: A function is said to be One-One if for every element in the domain there exists…

Q: Suppose that the three numbers r1, r2, and r3 are dis- tinct. Show that the three functions…

A:

Q: Please solve this linear algebra question for me.

A: We are given that v1, v2, v3, v4, v5 are linearly independent in F8.We need to show that v1, v2, v3,…

Q: Prove that the function : R-{1} →R- {2} defined by 2a f(x)= s bijective. 2 1

A:

Q: Let T: R" → R" be defined as T(x₁,x₂,...,xn) = (x₂ −X₁, X3 X₂, ..., x₁ - xn) of T Discuss the…

A: The matrix is invertible if the determinant of the matrix is non-zero. The matrix is diagonalizable…

Q: Prove that if A ϵ Mnxn(F) has two identical columns, then det(A) = 0.

A: Given: A∈Mn×nF i.e. A is a matrix of order n×n.   Consider a matrix with first two column as…

Q: Which of the following operators in R'are linear? 1. T(x) = (8x2, -5x, -9x) %3D 2 T(x) = (10x; - 7x2…

A:

Q: Prove directly that the functions f1(x) = 1, f2(x) = x, and f3(x) = x² = x² are linearly independent…

A: 27. The given functions are f1x=1, f2x=x and f3x=x2. For this we have to show that…

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A:

Q: 3. Construct a bijection f: [0, 1] → (0, 1) UN.

A:

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A:

Q: Find the linearization of ƒ(x) = 2/(1 - x) + saqrt(1 + x) - 3.1 at x = 0

A: Given,

Q: 10. Show that 1/x, x are linearly independent on (0, 0).

A:

Q: 3. Let T: M₂2 → R² be defined as T ( [])=(a - b, cd). Determine whether or not I' is a linear…

A: I have given the answer in the next step. Hope you understand that

Q: Let T be the linear thansformation from R³ to R4 defined by 1 -8 1 X1 1 3 2 X2 X2 -2 2 4 X3 X3 3 0…

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Q: Let A,X EM, (C) such that A is positive semidefinit and AX = XA Show that A¹/2X = XA¹/2.

A: Introduction: Definite matrix is significant in studying quadratic forms. Also, in Lyapunov…

Q: 2 2) Find a number t such that -3 is not linearly independent in R.

A:

Q: (b) Are the polynomials x + 5, x – 5, 2x +1 linearly independent in P1(R)? Explain.

A: The vectors a1, ..., an are called linearly independent if there are no non-trivial combination of…

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A: We need to examine the continuity of the given function f(x) at x=a.

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Q: Let f(z) = 3-1교2-8고 + 쯤. a) Compute the minimum and the maximum of f.

A: f(x)=19x3-13x2-83x+269

Q: Show that the set {1, x, x2, ..., xn} is linearly independent in Pn(F).

A:

Q: Suppose that T :C C is R-linear. Show that T is C-linear if and if T(iz) = iTz for all z.

A: First we describe the definition of C-linear function:

Q: t 31, 2021, 16:36 Dues the invense of the func Hion f cx)=x_3 exist?

A:

Q: Suppose that T: R2→ R2 is linear, T(1, 0) = (1, 4), and T(1, 1) = (2, 5). What is T(2,3)? Is T…

A: Given,

Q: Let f(x,y) = x - 5xy -y². Compute f(6,0), f(6, – 2), and f(b,c).

A: Solved 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.