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

question 39

Essay

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.

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Definitions:

Cohabitation

Cohabitation involves living together in a sexual relationship without being married.

Reciprocity

A social norm of responding to a positive action with another positive action, fostering mutual benefit and cooperation.

Romantic Partners

Individuals engaged in a significant intimate relationship, marked by feelings of affection, love, and commitment towards one another.

Celibate

Abstaining from marriage and sexual relations, often for religious, personal, or other reasons.