Linear Algebra Exam Questions with Answers

Linear Algebra Exam Questions with Answers 1.1 10. d. Is the statement "Two fundamental questions about a linear system involve existence and uniqueness" true or false? Explain. - Answer-True, because two fundamental questions address whether the solution exists and whether there is only one solution. 1.1 11. a. Is the statement "Two matrices are row equivalent if they have the same number of rows" true or false? Explain. - Answer-False, because if two matrices are row equivalent it means that there exists a sequence of row operations that transforms one matrix to the other. 1.1 11. b. Is the statement "Elementary row operations on an augmented matrix never change the solution set of the associated linear system" true or false? Explain. - Answer-True, because the elementary row operations replace a system with an equivalent system. 1.1 11. c. Is the statement "Two equivalent linear systems can have different solution sets" true or false? Explain. - Answer-False, because two systems are called equivalent if they have the same solution set. 1.1 11. d. Is the statement "A consistent system of linear equations has one or more solutions" true or false? Explain. - Answer-True, a consistent system is defined as a system that has at least one solution. 1.1 10. a. Is the statement "Every elementary row operation is reversible" true or false? Explain. - Answer-True, because replacement, interchanging, and scaling are all reversible.