Determine whether the statement below is true or false. Justify the answer. A basic variable in a linear system is a variable that corresponds to a pivot column in the coefficient matrix. Choose the correct answer below. OA. The statement is true. It is the definition of a basic variable. O B. The statement is false. A variable that corresponds to a pivot column in the coefficient matrix is called a free variable, not a basic variable. O C. The statement is false. Not every linear system has basic variables. O D. The statement is true. If a linear system has both basic and free variables, then each basic variable can be expressed in terms of the free variables.
Determine whether the statement below is true or false. Justify the answer. A basic variable in a linear system is a variable that corresponds to a pivot column in the coefficient matrix. Choose the correct answer below. OA. The statement is true. It is the definition of a basic variable. O B. The statement is false. A variable that corresponds to a pivot column in the coefficient matrix is called a free variable, not a basic variable. O C. The statement is false. Not every linear system has basic variables. O D. The statement is true. If a linear system has both basic and free variables, then each basic variable can be expressed in terms of the free variables.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Determine whether the statement below is true or false. Justify the answer.
A basic variable in a linear system is a variable that corresponds to a pivot column in the coefficient matrix.
Choose the correct answer below.
O A. The statement is true. It is the definition of a basic variable.
O B. The statement is false. A variable that corresponds to a pivot column in the coefficient matrix is called a free variable, not a basic
variable.
O C. The statement is false. Not every linear system has basic variables.
O D. The statement is true. If a linear system has both basic and free variables, then each basic variable can be expressed in terms of
the free variables.
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