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Practice: Creating a Zero Entry in a Matrix Row
To get a specific entry in an augmented matrix to be zero, determine the appropriate row operation that will eliminate the current value. This typically involves multiplying one row by a constant and adding it to the target row. For instance, if the first entry in row is and the first entry in row is , multiplying row by and adding it to row (documented as ) will result in a in the target position. Performing the arithmetic across all corresponding entries in the rows completes the operation and produces an equivalent matrix. Similarly, to eliminate a or in row when the first entry of row is , you would apply or , respectively.
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Ch.4 Systems of Linear Equations - Intermediate Algebra @ OpenStax
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Practice: Creating a Zero Entry in a Matrix Row
Example: Creating a Zero Entry in a Matrix Row
When organizing a matrix that represents project funding allocations, you are instructed to perform the row operation to simplify your data. Based on the standard notation for matrix operations, which action must you take?
A project manager is using a matrix to adjust a departmental budget. To update the total expenses for Department A () based on the labor costs of Department B (), they perform the row operation . Match each component of this notation to its correct role in the matrix transformation.
A budget analyst is using a matrix to reallocate funds between departments. If they apply the row operation , Row 1 is the destination row that will be updated with the new calculated values.
A logistics coordinator uses a matrix to represent the volume of goods moving between three regional hubs (, , and ). To simplify the data, they perform the row operation . According to the standard convention for matrix row operations, the results of this calculation are used to replace the original values in Row ____.
A project manager is using a matrix to track labor costs across two departments, represented by Row 1 () and Row 2 (). To update the budget, they need to perform the row operation . Arrange the following steps in the correct chronological order to execute this specific matrix transformation.
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A project manager is optimizing budget allocations using an augmented matrix. She needs to create a zero in the first entry of row 2, which currently has a value of 5. If the first entry in row 1 is 1, which standard row operation must she recall and apply to eliminate the 5?
A billing specialist is using a matrix to organize service charges for two different departments. To analyze the data, the specialist needs to create a zero in the first entry of the second row (). Assuming the first row () begins with a 1, match each possible entry value in the second row with the correct row operation required to eliminate it.
A logistics coordinator is using an augmented matrix to analyze delivery costs between two regions. If the lead entry in the first row () is and the first entry in the second row () is , the coordinator should apply the row operation to create a zero in the first entry of Row 2.
A small business owner is using an augmented matrix to analyze monthly expenses across two departments. To simplify the matrix, the owner needs to create a zero in the first position of the second row (). If the lead entry of the first row () is and the first entry of is , the owner must multiply by the constant ____ and add the result to to eliminate the value.
Inventory Management and Matrix Operations