Linear Algebra Conceptual Questions • What are the possible sizes of solution sets for linear systems?...

Linear Algebra Conceptual Questions
• What are the possible sizes of solution sets for linear systems?

• List as many things that are equivalent to a square matrix being nonsingular as you can.

• List as many things that are equivalent to a square matrix being singular as you can. (Should be basically the same as your list above except all opposites) • Give an example of a singular matrix that is NOT just the zero matrix.

• If a system has m equations and n unknowns where m < n, what are the possibilities for number of solutions to the system?

• Rephrase the question above, and your answer to it, in terms of the rank of the coefficient matrix for the system.

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Colby Messinger answered 1 year ago

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