24. a. Elementrary row operations on an augmentedmatrix never change the solutio

Question

24. a. Elementrary row operations on an augmentedmatrix never change the solution set of the associated linearsystem. false, it does changesomehow. (help me explain please!) b. Two matrices are row equivalent if they have the samenumber of rows. false, two matrices have the samesolution set if they are row equivalent c. An inconsistent system has more than onesolution.   false, inconsistent system has nosolution d. Two linear systems are equivalent if they have the samesolution set. True, (help me explain)
Check please! Are they correct? 24. a. Elementrary row operations on an augmentedmatrix never change the solution set of the associated linearsystem. false, it does changesomehow. (help me explain please!) b. Two matrices are row equivalent if they have the samenumber of rows. false, two matrices have the samesolution set if they are row equivalent c. An inconsistent system has more than onesolution.   false, inconsistent system has nosolution d. Two linear systems are equivalent if they have the samesolution set. True, (help me explain)
Check please! Are they correct? Are they correct?

Explanation / Answer

(a) True. Gaussian Elimination is based on the fact that youcan reduce an augmented system to a more simple associated linearsystem with the same solution set using elementary rowoperations. (b) False. A matrix A is row equivalent to matrix B if B canbe obtained from A using elementary row operations. (your reasoningis also correct, but row equivalence is defined for any matricies,not necessarily just augmented matricies with a solution set to asystem of linear equations) (c) False. Inconsistent System = No solution. (d) True. That's basically the definition of linear systemsbeing equivalent, if they have the same solution set.

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