4, x+y+z=12x+3y + 2z = 2ax + ay + 2az = 4
The given system of equations is,
x + y + z = 1 2 x + 3 y + 2 z = 2 a x + a y + 2 a z = 4
Write the system of equations in the form of AX = B .
[ 1 1 1 2 3 2 a a 2 a ] [ x y z ] = [ 1 2 4 ]
Now, the determinant of A is,
| A | = 1 ( 3 × 2 a − a × 2 ) − 1 ( 2 × 2 a − a × 2 ) + 1 ( 2 × a − a × 3 ) = 4 a − 2 a − a = a
Since, | A | ≠ 0 . Therefore, inverse of matrix A exists.
Hence, the system of equations is consistent.
The given system of equations is,
Write the system of equations in the form of
Now, the determinant of
Since,
Hence, the system of equations is consistent.
