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We have a set of $3$ linear equations in $3$ unknowns. $'X \equiv  Y'$ means $X$ and $Y$ are equivalent statements and $'X \not\equiv Y'$ means $X$ and $Y$ are not equivalent statements.

P: There is a unique solution.

Q: The equations are linearly independent.

R: All eigenvalues of the coefficient matrix are nonzero.

S: The determinant of the coefficient matrix is nonzero.

Which one of the following is TRUE?

  1. $P \equiv Q \equiv R \equiv S$
  2. $P \equiv R \not\equiv Q \equiv S$
  3. $P \equiv Q \not\equiv R \equiv S$
  4. $P\not\equiv Q \not\equiv R \not\equiv S$
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