this question deals with the “Laguerre Polynomials,” which are orthogonal with respect to the inner product hf, gi = Z ∞ 0 f(x)g(x) e −x dx. Use the fact that ∀ integers p, q ≥ 0 hx p , xq i = (p + q)! (“p plus q factorial”), to derive the first 4 (order 0, 1, 2, 3) orthonormal Laguerre Polynomials starting from elements of the standard polynomial basis {1, x, x2 , x3}. Let T ∈ L(C 7 ) be defined by T(z1, z2, z3, z4, z5, z6, z7) = (πz1+z2+z3+z4, πz2+z3+z4, πz3+z4, πz4, √ 7z5+z6+z7, √ 7z6+z7, √ 7z7) Let Bs(C 7 ) = {e1, e2, e3, e4, e5, e6, e7} be the standard basis of C 7 (a) (25 pts.) Find M(T, Bs(C 7(b) (25 pts.) Find the eigenvalues {λk}k=1,...,? (c) For each eigenvalue, λk: i. (30 pts.) Find the eigenspace E(λk, T) ii. (30 pts.) Find the generalized eigenspace G(λk, T)

Using the topic Gun Control and the Gun Control codebook complete the following tasks:Develop a theory.Develop a corresponding hypothesisIdentify the independent (IV) and dependent (DV) variables in your hypothesisOperationalize your independent and dependent variables.Hint: What are the attributes (categories) of your variable?Identify the level of measurement (LOM) of the independent and dependent variables in your hypothesis.Part 2: Using the Gun Control dataset complete the following tasks:Run frequencies on the variables:Religion.Education.OwnGun.CauseViolence.AmericanOwn.ConcealedWeapons.Summarize your findings.Part 3: Using the Gun Control dataset complete the following tasks:Run the measures of central tendency (MOCT) that correspond with each of the following variables’ levels of measurement (LOM):Religion.Education.OwnGun.CauseViolence.AmericanOwn.ConcealedWeapons.Summarize your findings.Part 4: Using the Gun Control dataset complete the following tasks:Run the measures of variability (MOV) that correspond with each of the following variables’ LOM:Religion.Education.OwnGun.CauseViolence.AmericanOwn.ConcealedWeapons.Summarize your findings.