Tax Returns Essay Example for Free

Tax Returns EssayConsider an comptroller who prepares tax returns. remember a form 1040EZ requires $12 in computer resources to process and 22 minutes of the comptrollers time. Assume a form 1040A takes $25 in computer resources and needs 48 minutes of the accountants time. If the accountant can spend $630 on computer resources and has 1194 minutes available, how many forms of 1040EZ and 1040A can the accountant process?SolutionLet x be the number of form 1040EZ that the accountant can processy be the number of form 1040A that the accountant can processThe system of equation required for this problem is12x + 25y 63022x + 48y 1194In augmented matrix formThe reduced form gives us the following behave of equations x + 2. 5y 52.5 x + 2.5(4.3) 52.5 x 41.7 y 4.3Answer The accountant can process at most 41.7 ( or 41) 1040EZ forms and at most 4.3 (or 4) 1040A forms.You are addicted the following system of bi analog equationsx y + 2z = 132x + y z = -6-x + 3y + z = -7a. Pr ovide a coefficient matrix corresponding to the system of linear equations.What is the inverse of this matrix?What is the transpose of this matrix?d. Find the determinant for this matrix.det(A) = (1)(1)(1) + (-1)(-1)(-1) + (2)(2)(3) (2)(1)(-1) (-1)(2)(1) (1)(-1)(3)det(A) = 19Calculate the following fora. A * Bb. -4Ac. ATSolve the following linear system using Gaussian elimination.Show work.3x + y z = -5-4x + y = 66x 2y + 3z = 2SolutionBackward substitution19/7 z = 76/7 z = 4y 4/7 z = -2/7 y = 2x+1/3 y 1/3 z = -5/3 x = -1Solve the following linear system for x using Cramers rule.Show work.x + 2y 3z = -222x 6y + 8z = 74-x 2y + 4z = 29SolutionThe coefficient matrix corresponding to the given system isand the break up column isdet(A) = (1)(-6)(4) + (2)(8)(-1) + (-3)(2)(-2) (-3)(-6)(-1) (2)(2)(4) (1)(8)(-2) = -10Plug-in the answer column to x column and get the determinantdet(X) = (-22)(-6)(4) + (2)(8)(29) + (-3)(74)(-2) (-3)(-6)(29) (2)(74)(4) (-22)(8)(-2) = -30Plug-in the answer column to y column and get the determinantdet(Y) = (1)(74)(4) + (-22)(8)(-1) + (-3)(2)(29) (-3)(74)(-1) (-22)(2)(4) (1)(8)(29) = 20Plug-in the answer column to z column and get the determinantdet(Z) = (1)(-6)(29) + (2)(74)(-1) + (-22)(2)(-2) (-22)(-6)(-1) (2)(2)(29) (1)(74)(-2) = -70By Cramers rule, the rootage to the system isx = -30 / -10 = 3y = 20 / -10 = -2z = -70 / -10 = 7