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Determine the principal P that must be invested at rate r = 6%, compounded monthly, so that $500,000 will be available for retirement in t = 19 years. (Round your answer to the nearest cent.) P= $ Solve the system of linear equations and check any solution algebraically. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express x, y, and z in terms of the real number a.) x+ y Z = x - 2y + 4z = 11 3y + 42 = 17 (x, y, z) Write the partial fraction decomposition of the rational expression. Check your result algebraically. x+ 3 X2 - X - 20 Use matrices to solve the system of equations (if possible). Use Gaussian elimination with back-substitution. (If there is no solution, enter NO SOLUTION. If there are infinitely many + solutions, express x, y, and z in terms of the real number a.) x + 2y - 22 = -26 4y + 22 = ol -x+y Z = (x, y, Z) = Write the partial fraction decomposition of the rational expression. Check your result algebraically, 5x X3-1