Question 3.3.4: The homogeneous linear system 47x1 + 73x2 + 56x3 + 21x4 = 0 ...

The homogeneous linear system

47 x_{1} + 73 x_{2} + 56 x_{3} + 21 x_{4} = 0

19 x_{1} + 81 x_{2}  –  17 x_{3}  –  99 x_{4} = 0

53 x_{1} + 62 x_{2} + 39 x_{3} + 25 x_{4} = 0

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of three equations in four unknowns necessarily has infinitely many solutions. The only question (which we could answer by reducing the system to echelon form) is whether the system has one, two, or three free variables.

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