Augmented matrix
A=⎣⎡13−4−1−1225x2−81−2x+2⎦⎤
R2=R2−3R1
⎣⎡10−4−1222−1x2−81−5x+2⎦⎤
R3=R3+4R1
⎣⎡100−12−22−1x21−5x+6⎦⎤
R2=R2/2
⎣⎡100−11−22−1/2x21−5/2x+6⎦⎤
R1=R1+R2
⎣⎡10001−23/2−1/2x2−3/2−5/2x+6⎦⎤
R3=R3+2R2
⎣⎡1000103/2−1/2x2−1−3/2−5/2x+1⎦⎤ I) no solution
x2−1=0x+1=0=>x=1
Ii) exactly one solution
x2−1=0=>x=±1
Iii) infinitely many solutions
x2−1=0x+1=0=>x=−1
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