Find the general solution for the system of equations using parameters as needed: r, s, t: x+y+2z=5 x+z=-2 2x+y+3z=3 Use of technology is okay, but must be documented carefully. All steps must be recorded except for the calculations, including any rewrite to matrix form. Include in your work the input to the technology, the command for the tech, document what technology you used, show the output. Be sure to answer the question (do not leave the "interpretation" of the output to your reader) a. Show the solution to the given system as a linear combination of column vectors using your chosen parameters. b. Give a basis for the solution space for

A small software corporation borrowed $292,500 to expand its software line. Some of the money was borrowed at 9%, some at 10%, and some at 12%. Use a system of equations to determine how much was borrowed at each rate if the annual interest was $29,900 and the amount borrowed at 10% was 22 times the amount borrowed at 9%. Solve the system using matrices. Step 1 Let the amount borrowed at 9% be x, the amount borrowed at 10% be y, and the amount borrowed at 12% be z. The total amount borrowed was $292,500. The total annual interest was $29,900. The amount borrowed at 10% was 2- times the amount borrowed at 9%. Write a set of equations using the information given. Convert the percentage to decimal fraction. x + y + z = 292,500 .09 x +.10 y + |.12 V z = 29,900 X x - y = 0 Write the associated augmented matrix for the given system of equations. Recall that since there are three equations in the system, the matrix will have three rows. Use the coefficients of x, y and z as entries of the…

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.)