1. Solve the system below using Gauss Jordan elimination. It is easiest to use matrices 21 - 02+2.3 = 5 201 + 22-23 = 1 321 +22+203 = 3 2. Use the rref feature on your calculators to show that the system below is inconsistent. 31 +32 +2x3 = 7 231 +262 +423 = 10 3.x1 + x2 +23 = 3 3. Use the rref feature on your calculators to show that the system represented by the matrix below has infinitely many solutions. Characterize the solutions. 2 -2 -5 -7 2 8 o 1 0 7 0 4 4. Use row reduction to find the inverse of the matrix below. 0 1 1 0 1 1 0 1 5. Solve the following linear programming problem graphically. A man operates a pushcart selling hotdogs and sodas. His cart can support 210 lbs. A hotdog and bun weighs 2 ounces and a soda weighs 8 ounces. He knows he must have at least 60 sodas and 80 hotdogs. He also needs at least one soda for every two hotdogs. Given that he makes a $2 profit on each hotdog and $1 on each soda, how many of each item should he carry to maximize his profits? Let x1 be the number of hotdogs and x2 be the number of sodas. 6. Graphically solve the LP Min z = 4.21 + 8x2 S.. 5x1 + 10x2 = 150 21 14 21 > 0 . Use the simplex method to solve the LP S.I. Max z = 1 + x2 4x +1+22 0 1. Solve the system below using Gauss Jordan elimination. It is easiest to use matrices 21 - 02+2.3 = 5 201 + 22-23 = 1 321 +22+203 = 3 2. Use the rref feature on your calculators to show that the system below is inconsistent. 31 +32 +2x3 = 7 231 +262 +423 = 10 3.x1 + x2 +23 = 3 3. Use the rref feature on your calculators to show that the system represented by the matrix below has infinitely many solutions. Characterize the solutions. 2 -2 -5 -7 2 8 o 1 0 7 0 4 4. Use row reduction to find the inverse of the matrix below. 0 1 1 0 1 1 0 1 5. Solve the following linear programming problem graphically. A man operates a pushcart selling hotdogs and sodas. His cart can support 210 lbs. A hotdog and bun weighs 2 ounces and a soda weighs 8 ounces. He knows he must have at least 60 sodas and 80 hotdogs. He also needs at least one soda for every two hotdogs. Given that he makes a $2 profit on each hotdog and $1 on each soda, how many of each item should he carry to maximize his profits? Let x1 be the number of hotdogs and x2 be the number of sodas. 6. Graphically solve the LP Min z = 4.21 + 8x2 S.. 5x1 + 10x2 = 150 21 14 21 > 0 . Use the simplex method to solve the LP S.I. Max z = 1 + x2 4x +1+22 0