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Question

4, x+y+z=12x+3y + 2z = 2ax + ay + 2az = 4

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Solution

The given system of equations is,

x+y+z=1 2x+3y+2z=2 ax+ay+2az=4

Write the system of equations in the form of AX=B.

[ 1 1 1 2 3 2 a a 2a ][ x y z ]=[ 1 2 4 ]

Now, the determinant of A is,

| A |=1( 3×2aa×2 )1( 2×2aa×2 )+1( 2×aa×3 ) =4a2aa =a

Since, | A |0. Therefore, inverse of matrix A exists.

Hence, the system of equations is consistent.


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