Determine if each of the following statements is true or false: 1) It is impossible for a system of linear equations to have exactly 1000 solutions. 2) There is no system of linear equations that is inconsistent for every choice of constant terms. 3) Any linear combination of solutions to a system of linear equations is again a solution for the original system.
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Statement 1: It is impossible for a system of linear equations to have exactly 1000 solutions. This statement is false. A system of linear equations can have any number of solutions, including 1000 solutions. For example, consider the system of equations: x + y Show more…
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