Find the solutions (x1, x2, x3) for the linear system with various parameters (a,b). 2x13x2ax3 = 1 2x13x2+2x3 = b 4x13x2+2x3 = 4 (a) a = 4, Vb Є R (b) a=2,b=1 " (c) a a = 2, Vb Є R = b + 1 Perform row reduction starting with the augmented matrix and ending with reduced row echelon form. Show each row reduction step. If the system has no solutions, explain why. If the system is consistent, find all solu- tions. In the case of infinitely many solutions, use parameters.

Let f(t) be a function on (0, oo). The Laplace transform of f is the function E defined by the integral F(s) = e St(t)dt. Use this definition to determine the Laplace transform of the foliowing function. f(1) = e -41 sin 3t The Laplace transform of f(t) is F(s)= (Type an expression using s as the variable.) It is defined for s> (Type an integer or a fraction.)

I painted a picture that is 4 inches longer than it is wide. If I put a I-inch frame around my picture, the area increases by 48 square inches. What are the dimensions of my picture?

You are designing a poster which has a border around the printed portion. The border is 2 inches wide on the left and right sides, and 3 inches wide on the top and bottom. The entire poster will be a total of 300 square inches, including the borders and printed portion combined.