True or False? In Exercises 59 and 60, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.
(a) A
(b) Every matrix is row-equivalent to a matrix in row- echelon form.
(c) If the row- echelon form of the augmented matrix of a system of linear equations contains the row [1 0 0 0 0], then the original system is inconsistent.
(d) A homogeneous system of four linear equations in six variables has infinitely many solutions.
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Elementary Linear Algebra (MindTap Course List)
- True or False? In Exercises 85 and 86, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriaste statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. a For the product of two matrices to be defined, the number of columns of the first matrix must equal the number of rows of the second matrix. b The system Ax=b. Is consistent if and only if b can be expressed as a linear combination of the columns of A, where the coefficients of the linear combination are a solution of the system.arrow_forwardTrue or False? In Exercises 73 and 76, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. a If an mn matrix B can be obtained from elementary row operations on an mn matrix A, then the column space of B is equal to the column space of A. b The system of linearity equations Ax=b is inconsistent if and only if b is in the column space of A.arrow_forwardTrue or False? In Exercises 41 and 42, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. a The zero matrix is an elementary matrix. b A square matrix is nonsingular when it an be written as the product ofelementary matrices. c Ax=O has only the trivial solution if and only if Ax=b has a unique solution for every n1 column matrix b.arrow_forward
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- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning