Question

Find conditions on k∈ℝ so that the system of linear equations
x1+x2−x3=1
2x1+3x2+kx3=3
x1+kx2+3x3=2
has

i) a unique solution;
ii) no solution;
iii) infinitely many solutions.
Hint: Use Gaussian elimination.

Answer 1

rank = 1 => unique solution

Answer 2

if u get last row as : 0 0 0 0
then infinitely many zeroes

Answer 3

if u get last row as : 0 0 0 x
then no solution

Answer 4

reduce it first