Question

Matrix Algebra

Given a system of the form -M1X1 + X2 = bt -m2X1 + X2 = b 2 where my, m2, 61, and b2 are constants, (a) Show that the system will have a unique solution if my # m2. (b) Show that if m1 = m2, then the system will be consistent only if b1 = b2. (c) Give a geometric interpretation of parts (a) and (b).

Answer 1

Rank Art. Hence it Rank ĽAIBI=1 mix+x=bl. -m24+x2=62 Ax=B. where. 1.**.53] Above system has unique soen it Rank A=2 ou A140 IAIS -m, + m2 70 ). mitma Hence system has. unique soln it mitm. ĽA IB] Augmeted mat sin - mi 1 bi - m2 1 ba R2 - Mex Rz & MaXR, 21= 15t Row Rosand Row 1. bi 0 - mitm2 -mba+Mabi mi = m2 bi mwa -m, mille m, [bi-be 1. Above system is consist it Rank A= Rank [AIB. Mito mi[bi-bal=0 bi-bra slbi=b2 if m, am2=0 then x2=61 x2=b2 > bi=be

system Represent two line in 2-dimension In @ it system has unique solution that two line intersect at a point which is solution of system In 6 m = M2 Rbl=bz then in one system Both Both equation represent same fine une rence every point on solution of above system.