Prof Double R "ONLY"
1g3xEBTRAY
fa-3pdr.pdf.docx1. -/
Find the augmented matrix representing the system of equations.
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2. -/Find the augmented matrix representing the system of equations.
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Interpret the row-reduced matrix as the solution of a system of equations. (Enter your answers as a comma-separated list. If the system is inconsistent, answer INCONSISTENT. If the system is dependent, parametrize the solutions in terms of the parameter t.)
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4. -/Use an appropriate row operation or sequence of row operations to find the equivalent row-reduced matrix.
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5. -/Use an appropriate row operation or sequence of row operations to find the equivalent row-reduced matrix.
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6. -/Solve the system of equations by the Gauss-Jordan method. (Enter your answers as a comma-separated list. If the system is inconsistent, answer INCONSISTENT. If the system is dependent, parametrize the solutions in terms of the parameter t.)
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7. -/Formulate the situation as a system of linear equations. Be sure to state clearly the meaning of each variable. Solve using the Gauss-Jordan method. State your final answer in terms of the original question. (If the system is inconsistent, answer INCONSISTENT. If the system is dependent, parametrize the solutions in terms of the parameters u and v.)
A large commercial farm needs 29,500 pounds of potash, 57,500 pounds of nitrogen, and 21,000 pounds of phosphoric acid. Three brands of fertilizer, GrowRite, MiracleMix, and GreatGreen, are available and contain the amounts of potash, nitrogen, and phosphoric acid per truckload listed in the table. How many truckloads of each brand should be used to provide the required potash, nitrogen, and phosphoric acid? trUCkloads of GrowRite truckloads of MiracleMix truckloads Of GreatGreen
(Pounds per GrowRite MiracleMix GreatGreen truckload)
Potash 400 600 700
Nitrogen 500 1000 1600
Phosphoric acid 300 400 500
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8. —/
Use the given matrix to find the expression.
At =
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9. —/Use the given matrix to find the expression.
10.
Use the given matrices to find the expression.
11. Find the matrix product.
12.-/2 pointsBerrFinMath1 3.4.007.
Find the matrix product.
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13.-/4 pointsBerrFinMath1 3.4.008.
Find the matrix product.
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14.-/15 pointsBerrFinMath1 3.4.009.
Rewrite the system of linear equations as a matrix equation AX —
7
15.-/17 pointsBerrFinMath1 3.4.010.
Rewrite the system of linear equations as a matrix equation AX
2X1 + — + X4 + = 6
— + X4 +
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16.-/18 pointsBerrFinMath1 3.4.012.
Formulate the situation in matrix form. Be sure to indicate the meaning of your rows and columns. Find the requested quantities using the appropriate matrix arithmetic.
A sports apparel company manufactures shorts, tee shirts, and caps in Costa Rica and Honduras for importation and sale in the United States. In
Costa Rica the labor costs per item are 80t per pair of shorts, 30t per tee shirt, and 45t per cap, while the costs of the necessary materials are $1.70 per pair of shorts, 95t per tee shirt, and $1.15 per cap. In Honduras the labor costs per item are 75t per pair of shorts, 20t per tee shirt, and 55t per cap, while the costs of the necessary materials are $1.40 per pair of shorts, 75t per tee shirt, and $1.05 per cap. Represent these costs as a labor cost matrix L and a materials cost matrix M. Use these matrices to find the total cost matrix C for these products in these countries. (Let the first row represent the cost, in pennies, in Costa Rica and the second row represent the cost, in pennies, in Honduras.) shorts tee shirt cap
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1. Solve the system by graphing. (Enter your answers as a comma-separated list. If the system is inconsistent, enter INCONSISTENT. If the system is dependent, enter DEPENDENT.) |
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x + y = 10 |
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x − y = 4 |
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(x, y) |
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2. Solve the system by the elimination method. (Enter your answers as a comma-separated list. If the system is inconsistent, enter INCONSISTENT. If the system is dependent, enter DEPENDENT.)
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3x + y = 15 |
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x + 2y = 10 |
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3. Solve the system by the elimination method. (Enter your answers as a comma-separated list. If the system is inconsistent, enter INCONSISTENT. If the system is dependent, enter DEPENDENT.)
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x + 2y = 10 |
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3x + 4y = 24
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4. Solve the system by the elimination method. (Enter your answers as a comma-separated list. If the system is inconsistent, enter INCONSISTENT. If the system is dependent, enter DEPENDENT.)
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2x + 5y = 67 |
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2x + 3y = 53 |
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(x, y) |
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Formulate the situation as a system of two linear equations in two variables. Be sure to state clearly the meaning of your x- and y-variables. Solve the system by the elimination method. Be sure to state your final answer in terms of the original question. A lawyer has found 60 investors for a limited partnership to purchase an inner-city apartment building, with each contributing either $6,000 or $12,000. If the partnership raised $498,000, then how many investors contributed $6,000 and how many contributed $12,000?
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$6,000 investors |
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$12,000 investors
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Formulate the situation as a system of two linear equations in two variables. Be sure to state clearly the meaning of your x- and y-variables. Solve the system by the elimination method. Be sure to state your final answer in terms of the original question. A jar contains 70 nickels and dimes worth $5.20. How many of each kind of coin are in the jar?
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nickels |
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dimes |
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Formulate the situation as a system of two linear equations in two variables. Be sure to state clearly the meaning of your x- and y-variables. Solve the system by the elimination method. Be sure to state your final answer in terms of the original question. The concession stand at an ice hockey rink had receipts of $10200 from selling a total of 4200 sodas and hot dogs. If each soda sold for $2 and each hot dog sold for $3, how many of each were sold?
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sodas |
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hot dogs |
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Carry out the row operation on the matrix.
R1 − R2 → R1 on
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Carry out the row operation on the matrix.
Interpret the augmented matrix as the solution of a system of equations. (Enter your answers as a comma-separated list. If the system is inconsistent, enter INCONSISTENT. If the system is dependent, enter DEPENDENT.)
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11. Solve the system by row-reducing the corresponding augmented matrix. (Enter your answers as a comma-separated list. If the system is inconsistent, enter INCONSISTENT. If the system is dependent, enter DEPENDENT.)
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12. Express the situation as a system of two equations in two variables. Be sure to state clearly the meaning of your x- and y-variables. Solve the system by row-reducing the corresponding augmented matrix. State your final answer in terms of the original question. For the final days before the election, the campaign manager has a total of $40,500 to spend on TV and radio campaign advertisements. Each TV ad costs $3000 and is seen by 10,000 voters, while each radio ad costs $500 and is heard by 2000 voters. Ignoring repeated exposures to the same voter, how many TV and radio ads will contact 142,000 voters using the allocated funds?
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TV ads |
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radio ads |
