7. (a) Use a matrix method to find the relationship between the constants a and b for which the system of equations u+2v +3w = a, u-v+w = 1, 2u + v+ 4w =b %3D has solutions. When a and b satisfy this relationship, find all of the solutions to this system in terms of a and write your answer in vector form. (b) In a market, the price of a share t seconds after the market opens is p(t) dollars. An analyst constructs a model which predicts that the price of this share should vary continuously with time according to the differential equation dp = p(t) - e. dt %3D If the initial price is $1, solve this differential equation to find p(t). Show that, according to the model, p(t) is increasing for all t > 0. When will the price of a share reach $1.25?

9) Solve the set of equations by finding the inverse of the coefficient matrix: x - 2y = 5 3x + y = 15 formation of vectors in

What volume of each of a 5% acid solution and a 65% acid solution should be combined to form 46 ml of a 50% solution? Set up the appropriate equations and solve the system using the inverse of the coefficient matrix. Combine O ml of the 5% acid solution withO mL of the 65% acid solution to form 46 mL of a 50% solution. (Type integers or decimals. Round the final answers to two decimal places as needed. Round all intermediate values to two decimal places as needed.)