Question

please explain every step. thanks

Consider the following system of linear equations ri (a) For what values of r and s is this system of linear equations inconsistent? (b) For what values of and s does this system of linear equations have infinitely many solutions? (ey For what values of and s does this system of linear equations have a unique solution?

Answer 1

Augmented matrix of the given system is [1 1 1 1 0 - 1 1 3 r 1 - 2 + x 3] almostequalto [1 0 0 1 - 1 - 2 1 2 r - 1 1 - 3 + s 2] R_2 rightarrow R_2 - R_1 R_3 rightarrow R_3 - R_1 almostequalto [1 0 0 1 - 1 0 1 2 r - 1/2 - 2 1 - 3 + s 1 + 3 - s] R_3 rightarrow R_3/2 - R_2 r - 1/2 - 2 = r - 5/2 (a) For inconsistent r - 5/2 = 0 = > r = 5 and 4 - s notequalto 0 = > s notequalto 4 (b) For infinite many solution r - 5/2 = 0 & 4 - s = 0 r = 5 & s = 4 (c) For unique solution r - 1/2 - 2 notequalto 0 = > r notequalto 5