Science:Math Exam Resources/Courses/MATH152/April 2022/Question A12/Solution 1

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This system has more variables than equations, so it will either have no solutions or infinitely many solutions. To see why the system could have 0 solutions, consider the possibility that is a matrix of 0s and is a non-zero vector.

Suppose now that there is at least one solution. Since there are two fewer equations than variables, there will be two free variables when solving the system, so the solutions will form a plane. (If there were only one free variable, they would form a line.)