Gaussian Elimination Method and Matrix Inverse and Matrix Equations

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Question 1: 92 -81 Solve the system . 12x 21y + -75 -23 Question 2: Solve the system . '{(,,,-,2z,=,6),(-3x,-, 10y,-,6z,=,7), (x,+, 3y,+,2z,=,-3):]' Question 3: The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 332 people entered the park, and the admission fees collected totaled 848.00 dollars. How many children and Your answer is number of children equals number of adults equals Question 4: Given the matrix 2 11 *5 27]' (a) does the inverse of the matrix exist? Your answer is (input Yes or No) : (b) if your answer is yes, write the inverse here: Question 5: Find the inverse of A = -30 -7] Question 6: Given the matrix - 1 1 - 1 . (a) does the inverse of the matrix exist? Your answer is (input Yes or No): b) if your answer is Yes, write the inverse as Question 7: Solve the system of equations -2x + 7y = 315 6x + 4y = 630 by converting to a matrix equation and using the inverse of the coefficient matrix. Question 8: Solve the system of equations 8x + ly = 811 [-5x - ly = - 508 by converting to a matrix equation and using the inverse of the coefficient matrix. Question 9: Write the system of equations ( -4x + 2y + 1z = -4 5x + 5y + 2z =3 5x - 5y + 2z = 1 as a matrix equation, that is, rewrite it in the form 1y = B where A = and B Question 10: solve the system of equations: ( 3x - 8y + z = - 20 -aty- z=3 x - 3y = -7 y = Question 11: Solve the system of equations: = 7),(-x + y -z= 0),(x -Zy = 5 ):]' Question 12: Solve the system of equations: {(3 x -6 y + z= -14), (-x + y -z= 3), (x -2 y = -4 ):]' Question 13: Maricopa's Success scholarship fund receives a gift of $ 135000. The money is invested in stocks, bonds, and erest, and stocks pay 11.5 % interest. Maricopa success invests $ 25000 more in bonds than in CDs. If the annual income from the investments is $ 8062.5 , how much was invested in each account? Maricopa Success invested $ in stocks . Maricopa Success invested $ in bonds. Maricopa Success invested $ in CDs