JEE Advanced 2018 Mathematics question
Let be the set of all column matrices such that and the system of equations (in real variables)
-x+2y+5z=
2x-4y+3z=
x-2y+2z=
has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for each ?
Answer: (A),(D)
Solution
The given coefficient matrix has determinant 0; the rows satisfy , so S is the plane . (A) Determinant : solvable for every right side: true. (B)
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