(1) Because r(A)=3, the basic analysis of linear equations Ax=0 has only one solution vector. Subtracting the two equations with known conditions, we can get A3-a 1 = (3,2,1,0)T, which is the solution of Ax=0. Besides, because of A65438. Therefore, A(a2+a3)=Aa2+Aa3=2b satisfies Aa2=Aa3=b, so A(a2+a3)/2=b can also be obtained, so (A2+A3)/2 = (2,2,2 2) T is a special solution of AX = B. According to the structure of solutions of non-homogeneous linear equations, 2. (3) Let X represent the quantity of waste products and X ~ B (500,0.01), so the mathematical expectation μ=np=5, and the variance σ=npq=4.95. According to the central limit theorem of independent identical distribution, y = (x-nμ)/(σ √ n) ~ n (0,65438) can be obtained.