Consistency of linear systems
Matrices and determinants (introductory) · Mathematics
Study notes
Q: Check consistency: (a) x+y=2, 2x+2y=4 (b) x+y=2, 2x+2y=5. (a) Second is 2× first: dependent. Augmented ranks equal (1=1 < 2): infinite solutions (y = 2-x). (b) Parallel lines (0 = 1 contradiction): ranks differ: no solution. Inconsistent.