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Linear Algebra

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) ______________________________

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

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

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 -- 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 Algebra - Vector Spaces

Let P be the set of all polynomials. Show that P, with the usual addition and scalar multiplication of functions, forms a vector space. I'm just no good at proofs. I know we are supposed to go through and prove the Vector Space Axioms and the C1 and C2 closure properties. I just don't think I'm doing it successfully. I'm just