Linear Algebra True-False

True or False? 1 Every Elementary Row Operation is reversible. 2 A 5 × 6 matrix has six rows. 3 The solution set of a linear system involving x1 , . . . , xn is a list of numbers (s1 , . . . , sn ) that makes each equation in the system a true statement. 4 Two fundamental questions about a linear system involve existence and uniqueness. September 3, 2021 1/6 True or False? 1 Every Elementary Row Operation is reversible. True- Necessary to keep the new matrix equivalent. 2 A 5 × 6 matrix has six rows. 3 The solution set of a linear system involving x1 , . . . , xn is a list of numbers (s1 , . . . , sn ) that makes each equation in the system a true statement. 4 Two fundamental questions about a linear system involve existence and uniqueness. September 3, 2021 2/6 True or False? 1 Every Elementary Row Operation is reversible. True- Necessary to keep the new matrix equivalent. 2 A 5 × 6 matrix has six rows. False- It is an array with 5 rows, 6 columns. 3 The solution set of a linear system involving x1 , . . . , xn is a list of numbers (s1 , . . . , sn ) that makes each equation in the system a true statement. 4 Two fundamental questions about a linear system involve existence and uniqueness. September 3, 2021 3/6 True or False? 1 Every Elementary Row Operation is reversible. True- Necessary to keep the new matrix equivalent. 2 A 5 × 6 matrix has six rows. False- It is an array with 5 rows, 6 columns. 3 The solution set of a linear system involving x1 , . . . , xn is a list of numbers (s1 , . . . , sn ) that makes each equation in the system a true statement. False- Trick question. The solution SET might be lots of possible solutions, not a single list/vector. 4 Two fundamental questions about a linear system involve existence and uniqueness. September 3, 2021 4/6 True or False? 1 Every Elementary Row Operation is reversible. True- Necessary to keep the new matrix equivalent. 2 A 5 × 6 matrix has six rows. False- It is an array with 5 rows, 6 columns. 3 The solution set of a linear system involving x1 , . . . , xn is a list of numbers (s1 , . . . , sn ) that makes each equation in the system a true statement. False- Trick question. The solution SET might be lots of possible solutions, not a single list/vector. 4 Two fundamental questions about a linear system involve existence and uniqueness. True. September 3, 2021 5/6 True or False? 1 Two matrices are row equivalent if they have the same number of rows. September 3, 2021 6/6 True or False? 1 Two matrices are row equivalent if they have the same number of rows. False. Row equivalent means that we can perform row operations on one of them to make the other. September 3, 2021 6/6 True or False? 1 Two matrices are row equivalent if they have the same number of rows. False. Row equivalent means that we can perform row operations on one of them to make the other. 2 Elementary row operations on an augmented matrix never changes the solution set to the associated system. September 3, 2021 6/6 True or False? 1 Two matrices are row equivalent if they have the same number of rows. False. Row equivalent means that we can perform row operations on one of them to make the other. 2 Elementary row operations on an augmented matrix never changes the solution set to the associated system. True. September 3, 2021 6/6 True or False? 1 Two matrices are row equivalent if they have the same number of rows. False. Row equivalent means that we can perform row operations on one of them to make the other. 2 Elementary row operations on an augmented matrix never changes the solution set to the associated system. True. 3 Two equivalent linear systems can have different solution sets. September 3, 2021 6/6 True or False? 1 Two matrices are row equivalent if they have the same number of rows. False. Row equivalent means that we can perform row operations on one of them to make the other. 2 Elementary row operations on an augmented matrix never changes the solution set to the associated system. True. 3 Two equivalent linear systems can have different solution sets. False September 3, 2021 6/6 True or False? 1 Two matrices are row equivalent if they have the same number of rows. False. Row equivalent means that we can perform row operations on one of them to make the other. 2 Elementary row operations on an augmented matrix never changes the solution set to the associated system. True. 3 Two equivalent linear systems can have different solution sets. False 4 A consistent system of linear equations has one or more solutions. September 3, 2021 6/6 True or False? 1 Two matrices are row equivalent if they have the same number of rows. False. Row equivalent means that we can perform row operations on one of them to make the other. 2 Elementary row operations on an augmented matrix never changes the solution set to the associated system. True. 3 Two equivalent linear systems can have different solution sets. False 4 A consistent system of linear equations has one or more solutions. True. September 3, 2021 6/6 True or False? 1 Two matrices are row equivalent if they have the same number of rows. False. Row equivalent means that we can perform row operations on one of them to make the other. 2 Elementary row operations on an augmented matrix never changes the solution set to the associated system. True. 3 Two equivalent linear systems can have different solution sets. False 4 A consistent system of linear equations has one or more solutions. True. September 3, 2021 6/6