Question: Can a matrix whose entry is 0 on the diagonal be solved? Explain why or why not. What would you do to remedy the situation?

  1. Can a matrix whose entry is 0 on the diagonal be solved? Explain why or why not. What would you do to remedy the situation?
  2. Can any matrix be written as a system of linear equations? Explain why or why not. Explain how to write that system of equations.
  3. Does every 22 matrix have an inverse? Explain why or why not. Explain what condition is necessary for an inverse to exist.
  4. Examining Cramer's Rule, explain why there is no unique solution to the system when the determinant of your matrix is 0. For simplicity, use a 22 matrix.

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