Question

For what values of m and n the following system of linear equations has no solution? ( 3x + y + 22 =2 3-2x+2y=3z = 1 (x -y + mzan a) m= &n=- b) m = 2 & n - 1 2 d) m= & ner c) m &nER

Answer 1

-given system of equations 3x +y +22 =2 s. 2x try-37 21 1 0 any tmzan co-efficient matrix of the system o Tла is A 1-2 2 -3 l and corresponding augmented matrix 3 21 20 À = 1 1 -2 2 -3 I I LI-I mim Let us on apply elementary row operation -2 2 -3 1 1 R2 = R2 +267 R₂ R₃-R1 5' 13 23:22 7 Io / m-zin - 2 - 1 R = R₂ +2 R2 0813 - 53 73 Io 0 m 3 nt 2

If m-3 20 ie ma 3 Then sana of A is a (no. of non zero rows) If m - 30 mts to ie nt 2 en rank of Ā Is 3 (noo. of non zeno rows) In that cose, raka & rank Ā 7 The system of eauertion is & inconsistent Hence the system has no. solution. Therefore the system of linear ecuation hos no salution if m=3 & net Hence Ans: m=s, ant -