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Linear Algebra

Give a linear equation that expresses volume,V,in terms of Temperature, T

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

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 help

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

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. :)

Matrix Theory

A) Let A be a positive definite matrix. Show that X has a unique positive square root. That is, show that there exists a unique positive matrix X such that X^2 =A. B) How many square roots can a positive definite matrix have?

Matrix Theory

Suppose A is diagonalizable with distinct eigenvalues... See attached file for full problem description.

Antisymmetric relations

Let R and S be antisymmetric relations on a set A. Does R union S have to be antisymmetric also? Give a counterexample if the answer is no and proof if it is yes.

Matrix Theory/ Isometries

Suppose A is a unitary matrix. (a) Show that there exists an orthonormal basis B of eigenvectors for A. (b) Let P be the associated change-of-basis matrix. Explain how to alter B such that P lies in SU(n).

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