The equations `x + 2y + 3z = 1,2x + y + 3x = 2, 5x + 5y + 9 z = 5` have

Options

A. unique solution
B. infinite many solution
C. inconsistent
D. None of these

Answer

A

Explanation

The given system of equatins in the matrix form are written as below.
`[{:(1,2,3),(2,1,3),(5,5,9):}] [{:(,x),(,y),(,z):}] = [{:(,1),(,2),(,3):}]`
Let `A = [{:(,1,2,3),(,2,1,3),(,5,5,9):}]`
Now , `|A| = |{:(,1,2,3),(,2,1,3),(,5,5,9):}|`
` = 1(9-15)-2(18-15) + 3(10-15)`
` = 3ne 0`
When know that if `|A| ne 0` , then the system of equation has unique solution.