Answer:
Never
Never
Never
Step-by-step explanation:
The equations given are
2x1−6x2−4x3 = 6 ....... (1)
−x1+ax2+4x3 = −1 ........(2)
2x1−5x2−2x3 = 9 ..........(3)
the values of a for which the system of linear equations has no solutions
Let first add equation 1 and 2. Also equation 2 and 3. This will result to
X1 + (a X2 - 6X2) - 0 = 5
And
X1 + (aX2-5X2) + 2X3 = 8
Since X2 and X3 can't be cancelled out, we conclude that the value of a is never.
a unique solution,
Let first add equation 1 and 2. Also equation 2 and 3. This will result to
X1 + (a X2 - 6X2) - 0 = 5
And
X1 + (aX2-5X2) + 2X3 = 8
The value of a = never
infinitely many solutions.
Divide equation 1 by 2 we will get
X1 - 3X2 - 2X3 =3
Add the above equation with equation 3. This will result to
3X1 - 8X2 - 4X3 = 12
Everything ought to be the same. Since they're not.
Value of a = never.
