Chapter 2.6, Problem 4ES

9. Solve the differential equation: 10. Find the general solution of dy + y = 0. dy 33 dx 3x².

3. Differentiate f(x) = x² sin(x). 4. Evaluate the limit: sin(2x) lim x

1. Solve for x in the equation: 2. If A = (1/3 2/) 4 x³-3x²+4=0 find the determinant of A.

if a=2 and b=1 1) Calculate 49(B-1)2+7B−1AT+7ATB−1+(AT)2 2)Find a matrix C such that (B − 2C)-1=A 3) Find a non-diagonal matrix E ̸= B such that det(AB) = det(AE)

1.2.17. (!) Let G,, be the graph whose vertices are the permutations of (1,..., n}, with two permutations a₁, ..., a,, and b₁, ..., b, adjacent if they differ by interchanging a pair of adjacent entries (G3 shown below). Prove that G,, is connected. 132 123 213 312 321 231

Prove that Pleas -- Pleas A collection, Alof countinoes Sunction on a toplogical spacex separetes Point from closed setsinx (f the set S" (V) for KEA and V open set in xx from base for Top onx. @If faixe A} is collection of countinuous fancton on a top space X Wich Separates Points from closed sets then the toplogy on x is weak Top logy.