Find the steadystate vector for the matrix below. 0.6 0.3 0.3 P: 0.1 0.4 0.1 0.3 0.3 0.6 q = D (Type an integer or simplied fraction for each matrix element.) The weather in Columbus is either good, indifferent, or bad on any given day. If the weather is good today, there is a 40% chance it will be good tomorrow, a 30% chance it will be indifferent, and a 30% chance it P = 0-3 0-2 0-3 will be bad. If the weather is indifferent today, there is a 50% chance it ()3 Q3 05 will be good tomorrow, and a 20% chance it will be indifferent. Finally, if the weather is bad today, there is a 10% chance it will be good tomorrow and a 30% chance it will be indifferent. The stochastic matrix for this situation is shown to the right. In the long run, how likely is it for the weather in Columbus to be indifferent on a given day? 0.4 0.5 0.1 E In the long run, how likely is it for the weather in Columbus to be indifferent on a given day? El% (Round to the nearest integer as needed.) Find formulas for the current i and the voltage vc for the circuit described by the equation below, assuming R1 = 1 ohm, R2 = 0.25 ohm, C = 0.2 farad, and L = 0.25 henry. The initial current is 0 amp, and the initial voltage is 10 volts. R2 VC (R1 C) in (t) = ] and vc(1) =Solve the initial value problem x'(t) =Ax(t) fortzO, with x(0) = (2,1). Classify the nature of the origin as an attractor, repeller, or saddle point of the dynamical system described by x' = Ax. Find the directions of greatest attraction and/or repulsion. 1o 2 A: 5 -17 Solve the initial value problem. X\") =