If the system of linear equations
is consistent, then
is consistent, then
- A.
- B.
- C.
- D.
Show answer and solution
Correct option: A
Solution
For consistency, the determinant of the augmented matrix must satisfy the condition that the system has no contradictions. Notice that 2×(row 1) + 1×(row 2) + 1×(row 3) gives:
Coefficients of x: 2(1) + 0 + (-2) = 0
Coefficients of y: 2(-4) + 3 + 5 = 0
Coefficients of z: 2(7) + (-5) + (-9) = 0
Since the left-hand side becomes 0 identically, the right-hand side must also equal zero: 2g + h + k = 0.
Coefficients of x: 2(1) + 0 + (-2) = 0
Coefficients of y: 2(-4) + 3 + 5 = 0
Coefficients of z: 2(7) + (-5) + (-9) = 0
Since the left-hand side becomes 0 identically, the right-hand side must also equal zero: 2g + h + k = 0.
[JEE Main 2019 · 9 Jan · Shift II]