Subjects linear algebra

Linear Algebra True False 569E8F

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Linear Algebra True False 569E8F


1. The statement "Using Cramer's Rule involves computing determinants for both the coefficient matrix and matrices formed by replacing columns with constant vectors" is TRUE. Explanation: Cramer's Rule solves a system of linear equations by calculating the determinant of the coefficient matrix and determinants of matrices formed by replacing one column at a time with the constants vector. 2. The statement "The graphical method for solving linear programming problems is only applicable to problems with two decision variables" is TRUE. Explanation: The graphical method works only in two dimensions, so it applies only when there are two decision variables. 3. The statement "Cramer's Rule is particularly useful for large systems of equations" is FALSE. Explanation: Cramer's Rule is computationally expensive for large systems and is generally used for small systems (like 2x2 or 3x3). 4. The statement "In linear programming, redundant constraints are those that do not alter the feasible region" is TRUE. Explanation: Redundant constraints do not affect the feasible region because they are implied by other constraints. Final answers: 1. TRUE 2. TRUE 3. FALSE 4. TRUE