linear expansion is defined from the equation given in OPTION C.
<<<<<<<<Option C
linear expansion is defined from the equation 6. Linear expansion (a) is defined form the equation...
3. The linear expansion coefficient is defined by AL/L = a AT. Consider a material for which a is not constant but is a function of temperature: a (T) = 2o + QT where T is the Kelvin temperature and do = 10-5 K-1 Q = 10-7 K2 A bar of this material has a length 1.00 meters at T = 273 K. At what temperature will its length be increased by one percent? (25 points)
Let LA be the linear map from R2 to R2 defined by LA (i) = Av, and let LB be the linear map from R2 to IR2 defined by LB(T)-Bv where A -6 36 -1 6 and B-(1 0 The composition LA O LB is again a linear map Lc determined by a (2 x 2)-matrix C, such that Calculate C C- Let LA be the linear map from R2 to R2 defined by LA (i) = Av, and let...
us equation, L (y(x))-0. Prove that o a solution eneous equation, C(y(z))g(z). Is a hy or why not? 1. Let C be the linear operator defined as follows. (a) Let v,.. ,n be the solutions of the homogeneous equation, D an arbitrary linear combination, ciyi+..nn is also a solution. , c(y(z)) 0, Prove that (b) Let vi,. n be the solutions of the non-homogeneous equation, Cl) ga). Is a linear combination, ciy nyn also a solution? Why or why not?...
1 6. The general form of a linear, homogeneous, second-order equation with constant coefficients is dy dy form. ns (b) Show that if q关0, then the origin is the only equilibrium point of the sys (c) Show, that if q关0, then the only solution of the second-order equation constant is y(t) = 0 for all 1.
(1) Let w1, be a k-form and w2 be an l- form, both defined in an open subset UC R3. Let d : /\k (U)-ל ЛК +1 (U) be the exterior derivative of differential forms. (a) Show that d is a linear transformation of vector spaces. (b) Show that (c) Show that (d) Show that d(w) -d(d(w)) 0 for every k-form w, i.e. the map is the zero map (1) Let w1, be a k-form and w2 be an l-...
Consider the following nonhomogeneous linear differential equation ay 6) + by(s) + cy!4) + dy'"' + ky'' + my' + ny=3x²3x - 7cos +1 where coefficients a, b, c, d, k, m, n are constant. Assume that the general solution of the associated homogeneous linear differential equation is YAEC,+Ce**+ c xe** + c.xe3* + ecos What is the correct form of the particular solution y of given nonhomogeneous linear differential equation? Yanitiniz: o Yo=Ax*e** + Ex + F **+Cxcos() +oxsin()+Ex+F...
Identify the equation as homogeneous, Bernoulli, linear coefficients, or of the form y' = G(ax + by). 8tx dx - (t? - x?) dt = 0 Select all that apply. A. the form y' = G(ax + by) B. linear coefficients C. homogeneous D. Bernoulli
A Linear Equation of the form Ax+By=C, where A and B are not both zero, is in the standard form. Find the slope and y-intercept in terms of A, B, and C.
PART C ONLY! Thank you. 14. Fix a non-zero vector n R". Lot L : Rn → Rn be the linear mapping defined by L()-2 proj(T), fa TER or all (a) Show that if R", Such that oandj-n -0, then is an eigenvector of L What is its cigenvaluc? (b) Show that is an cigenvector of L. What is its cigenvalue? (c) What are the algebraic and geometric multiplicities of all cigenvalues of L? 14. Fix a non-zero vector n...
(6) In R3, let W be the set of solutions of the homogeneous linear equation r + 2y +3z 0. Let L be the set of solutions of the inhomogeneous linear equation (a) Define affine subspace of a vector space. (b) Prove that L is an affine subspace of R3 (c) Compute a vector v such that L = v + W (6) In R3, let W be the set of solutions of the homogeneous linear equation r + 2y...