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 A is an m xn matrix and B is an nx r matrix, then the product AB is an m xr matrix. O True, the number of elements in a column of the first matriix must be equal to the number of elements in a row of the second matrix. O False, the number of elements in a column of the first matrix must be equal to the number of elements in a row of the second matrix. O True, the number of elements in a row of the first matrix must be equal to the number of elements in a column of the second matrix. O False, the number of elements in a row of the first matrix must be equal to the number of elements in a column of the second matrix. (b) The matrix equation Ax = b, where A is the coefficient matrix and x and b are column matrices, can be used to represent a system of linear equations. O False, it can only be used to represent a system where x = 0, the zero column matrix. O False, it can only be used to represent a system of nonlinear equations. O False, it can only be used to represent a system where b = 0, the zero column matrix. O True, A represents the coefficients, x represents the variables, and b represents the constant terms on the right hand side of the system of equations.
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 A is an m xn matrix and B is an nx r matrix, then the product AB is an m xr matrix. O True, the number of elements in a column of the first matriix must be equal to the number of elements in a row of the second matrix. O False, the number of elements in a column of the first matrix must be equal to the number of elements in a row of the second matrix. O True, the number of elements in a row of the first matrix must be equal to the number of elements in a column of the second matrix. O False, the number of elements in a row of the first matrix must be equal to the number of elements in a column of the second matrix. (b) The matrix equation Ax = b, where A is the coefficient matrix and x and b are column matrices, can be used to represent a system of linear equations. O False, it can only be used to represent a system where x = 0, the zero column matrix. O False, it can only be used to represent a system of nonlinear equations. O False, it can only be used to represent a system where b = 0, the zero column matrix. O True, A represents the coefficients, x represents the variables, and b represents the constant terms on the right hand side of the system of equations.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.3: Matrix Algebra
Problem 85E: Determine if the statement is true or false. If the statement is false, then correct it and make it...
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Transcribed Image Text: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 A is an m xn matrix and B is an n x r matrix, then the product AB is an m xr matrix.
O True, the number of elements in a column of the first matrix must be equal to the number of elements in a row of the second matrix.
O False, the number of elements in a column of the first matrix must be equal to the number of elements in a row of the second matrix.
O True, the number of elements in a row of the first matrix must be equal to the number of elements in a column of the second matrix.
O False, the number of elements in a row of the first matrix must be equal to the number of elements in a column of the second matrix.
(b) The matrix equation Ax = b, where A is the coefficient matrix and x and b are column matrices, can be used to represent a system of linear equations.
O False, it can only be used to represent a system where x = 0, the zero column matrix.
O False, it can only be used to represent a system of nonlinear equations.
O False, it can only be used to represent a system where b = 0, the zero column matrix.
O True, A represents the coefficients, x represents the variables, and b represents the constant terms on the right hand side of the system of equations.
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