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## Main Question or Discussion Point

(1) Show that the space R over the field of rational numbers Q with the usual operations is infinite dimensional.

(2) Find the values of lambda and μ so that the system

2x1 + 3x2 + 5x3 = 9

7x1 + 3x2 − 2x3 = 8

2x1 + 3x2 + lamdax3 = μ

has (i) no solution, (ii) a unique solution, and (iii) an infinite number of

solutions.

Hints:::(2) (i) lamda= 5, μ [tex]\neq[/tex] 9 (ii) lamda [tex]\neq[/tex] 5, μ arbitrary (iii) lamda = 5, μ = 9.

(2) Find the values of lambda and μ so that the system

2x1 + 3x2 + 5x3 = 9

7x1 + 3x2 − 2x3 = 8

2x1 + 3x2 + lamdax3 = μ

has (i) no solution, (ii) a unique solution, and (iii) an infinite number of

solutions.

Hints:::(2) (i) lamda= 5, μ [tex]\neq[/tex] 9 (ii) lamda [tex]\neq[/tex] 5, μ arbitrary (iii) lamda = 5, μ = 9.