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Solve x-y+z=22x+3y-4z=-43x+y+z=8By using determinant method |
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Answer» Answer x+y+2z=4 2x+2y+4z=8 3x+3y+6z=12 By DETERMINANT method: ⎝ ⎜ ⎜ ⎛
1 3
1 2 3
2 4 6
⎠ ⎟ ⎟ ⎞
× ⎝ ⎜ ⎜ ⎛
x y z
⎠ ⎟ ⎟ ⎞
= ⎝ ⎜ ⎜ ⎛
4 8 12
⎠ ⎟ ⎟ ⎞
D= ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣
1 2 3
1 2 3
2 4 6
∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣
=0 Similarly, D 1
,D 2
,D 3
=0 As they all are 0 the set of equations will have INFINITE solutions. We can consider x and y as free VARIABLES... x=α;y=β Thus, the solution set is (α,β, 2 4−α−β
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