Example 2.2.6 (again)
In a square linear system (n equations in n unknowns), if the coefficient matrix A has rank n, then it is invertible and
AX = B A-1AX = A-1B IX = A-1B
the solution to the linear system is
X = A-1B
and the solution is [necessarily] unique.
If rank A < n , then A-1 does not exist and the system is either inconsistent or has infinitely many solutions, but not a unique solution.
Example 2.3.2
Solve the linear system
The unique solution to the linear system is
Check by substituting the solution into the left side of the linear system:
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