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    Linear Algebra

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    Linear Algebra: Linear Mapping

    Consider the following linear mapping from C[-pi,pi] into itself: L(f)=integral from -pi to pi of G(x),h(y),f(y)dy for any function f(x) in C[-pi,pi]. Here G(x), H(x) are given continuous functions. Find a function f such that L*f=lambda*f for some lambda and find the value of lambda. This is a generalization of the notion

    Linear Algebra: Vector Spaces

    Consider R2 with the following rules of multiplications and additions: For each x=(x1,x2), y=(y1,y2): x+y=(x2+y2,x1+y1) and for any scalar alpha, alpha*x=(alpha*x1, alpha*x2) Is it a vector space, if not demonstrate which axioms fail to hold. Also, show that Pn- the space of polynomials of order less than n is a vector spac

    Linear Algebra: Matrix of Transformation

    Are the following examples linear transformations from p3 to p4? If yes, compute the matrix of transformation in the standard basis of P3 {1,x,x^2} and P4 {1,x,x^2,x^3}. (a) L(p(x))=x^3*p''(x)+x^2p'(x)-x*p(x) (b) L(p(x))=x^2*p''(x)+p(x)p''(x) (c) L(p(x))=x^3*p(1)+x*p(0)

    Linear Algebra: Find a Vector in a Basis

    In the standard basis of P3 (i.e. {1,x,x^2}) p(x)=3-2x+5x^2, that is, it has coordinates p=(3,-2,5). Find the coordinates of this vector (polonomial) in the basis {1-x,1+x,x^2-1}

    Linear Alegbra: Span of Dimension

    What is the span of the dimension of... _______________________ over P3 v1=x^2, v2=1-x^2, v3=1 _______________________ over C[0,1] v1=cosx, v2=cos2x, v3=1 ___________________________ over R3, v1=(2,2,1),v2=(-3,0,-1),v3=(-4,2,-1) ______________________________

    Finding the slope of a linear equation.

    FIND THE SLOPE OF THIS EQUATION: 8x-2y= -48 Is the answer 4, -4, -6 or 6? Please explain how to solve the equation step by step and how to find the slope, also.

    Nonisomorphic Central Extensions

    Describe all nonisomorphic central extensions of Z_2 x Z_2 by a cyclic group Z_n for arbitrary n, meaning central extensions of the form: 1 --> Z_n --> G --> Z_2 x Z_2 --> 1

    Linear Algebra : Zero Matrix Proof

    Let A be a 2 x 2 matrix with A^3 = O. Prove that A^2 = O. Where O is the zero matrix. (Note: I've said nothing about the invertibility of A, it may or may not be invertible).

    Working with linear equations

    This is the first question of a 4 part problem. I just need help with how to start it. above is the 1st question to below problem: In some experiments, tathered data suggest that volume of gas and temperature are related quantities. In one particular experiment, at a temp. of -30 degrees C, the volume of a gas was measured t

    Differential Equations: Matrices and Eigenvalues

    For this problem please state the method you used and show the work required to obtain the answer. Find the general solution for each of the systems: (this is a matrix) X' = 1 0 0 2 1 -2 *X 3 2 1 this matrix has a parenthesis and a X outside of it.

    Linear Algebra: Factoring, Real and Complex Zeroes

    1. Factor the following polynomial y = 3x4 — 22x3 + 31x2 + 40x —16 2. Find the real solutions of y = x3 + 8x2 + 1 lx — 20 3. Solve the equation in the complex number system. 10x2 + 6x +1= 0 4. Form a polynomial with real coefficients having the given degree and zeros. Degree: 5 Zeros: 1, multiplicity 3; 1 + i

    Linear Algebra: Basis of a Subspace

    Please see the attached file for the fully formatted problem. Find the basis of a subspace, which is intersection of U and V, where U and V are the span of....

    Algebra: Linear Equations Completely Factored

    Please see the attached file for the fully formatted problems. 1. If x and y are both positive and x/y = y/(x+y), then x can be written in terms of y as? 2. If 65X = 4ax | s true for all real X then? 3. Completely factor 14n4 + 21n3 - 14n2 4. Find the equation of the line with slope m= ¾ and having its y-intercept at 1

    Calculating linear equations from planes

    The points on a plane: A(-3;2) and B(1.5;-3) are included in a parallel right to another one which crosses point at P(-2;-4) Find: a) The equation of this last right b) The equation of the right which passes through the origin and is perpendicular to both of them

    Systems of Linear Equations Word Problem

    Please help with the following problem that involves systems of linear equations. A cookie company makes three kinds of cookies, peanut butter, sugar,and oatmeal packaged in small, medium, and large boxes. The small box contains 1 dozen peanut butter and 1 dozen sugars; the medium box contains 2 dozen peanut butters, 1 dozen

    Industrial Application Images

    The two images below shows one of our attempts to come up with the rotation angle required. I believe that it does not work because we are using first order trig which assumes symmetry . Please comment on this assumption and or why it does not work. See attachment To Whom It May Concern: I am trying to solve the followi

    Linear Algebra -- Inner Product Spaces

    In C[-pi, pi] with inner product defined by (6), show that cos mx and sin nx are orthogonal and that both are unit vectors. Determine the distance between the two vectors. (6) (f,g) = (1/pi)* the integral from -pi to +pi of f(x)g(x)dx This is all from Linear Algebra With Applications by Steven J. Leon, Sixth Edition. Than

    Linear Algebra -- Orthonormal Sets

    Please see problem #1 of the attachment. If you show me how to do #1 (the answers are a and d, by the way) I'll probably be able to do #2. Thanks!

    Linear Algebra -- Linear Transformations

    Determine whether the following are linear transformations from C[0,1] into R^1. L(f) = |f(0)| L(f) = [f(0) + f(1)]/2 L(f) = {integral from 0 to 1 of [f(x)]^2 dx}^(1/2) Thanks so much. :)

    Linear Transformations: Example Problems

    Please help. I always have a hard time with Linear Algebra. What's the difference between mapping from R3 into R2 and mapping from R2 into R3? Why is the following not a linear transformation from R3 into R2? L(x) = (1 + x1, x2)^T And why is this one not a linear transformation from R2 into R3? L(x) = (x1, x2, 1)^T Th