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.

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.

ganeshie8 · Answer

rank = 1 => unique solution

ganeshie8 · Answer

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

ganeshie8 · Answer

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

ganeshie8 · Answer

reduce it first