Solve the problem.
-A mathematician has found 5 solutions to a homogeneous system of 40 equations in 42
variables. The 5 solutions are linearly independent and all other solutions can be
constructed by adding together appropriate multiples of these 5 solutions. Will the system
necessarily have a solution for every possible choice of constants on the right side of the
equation? Explain.

Question

Solve the problem.
-A mathematician has found 5 solutions to a homogeneous system of 40 equations in 42 
variables. The 5 solutions are linearly independent and all other solutions can be
constructed by adding together appropriate multiples of these 5 solutions. Will the system
necessarily have a solution for every possible choice of constants on the right side of the
equation? Explain.

Quizplus · Accepted Answer

The Answer of Solve the problem.
-A mathematician has found 5 solutions to a homogeneous system of 40 equations in 42 
variables. The 5 solutions are linearly independent and all other solutions can be
constructed by adding together appropriate multiples of these 5 solutions. Will the system
necessarily have a solution for every possible choice of constants on the right side of the
equation? Explain.

Solve the Problem. -A Mathematician Has Found 5 Solutions to a Homogeneous System