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?
- $P \equiv Q \equiv R \equiv S$
- $P \equiv R \not\equiv Q \equiv S$
- $P \equiv Q \not\equiv R \equiv S$
- $P\not\equiv Q \not\equiv R \not\equiv S$