Let S be the set of all column matrices [ array l b_ 1 b_ 2 b_ 3 array ] such that b 1 …
Mathematics · JEE Advanced · NTA Exams — Matrices and Determinants
Let S be the set of all column matrices \[\left[\begin{array}{l}
b_{1} \\
b_{2} \\
b_{3}
\end{array}\right]\] such that
b1, b2, b3 ∈ \(\mathbb{R}\) and the system of equations (in real variables)
–x + 2y + 5z = b1
2x – 4y + 3z = b2
x – 2y + 2z = b3
has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for each \[\left[\begin{array}{l} b_{1} \\ b_{2} \\ b_{3} \end{array}\right]\]∈S?
b1, b2, b3 ∈ \(\mathbb{R}\) and the system of equations (in real variables)
–x + 2y + 5z = b1
2x – 4y + 3z = b2
x – 2y + 2z = b3
has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for each \[\left[\begin{array}{l} b_{1} \\ b_{2} \\ b_{3} \end{array}\right]\]∈S?
- x + 2y + 3z = b1, 4y + 5z = b2 and x + 2y + 6z = b3
- x + y + 3z = b1, 5x + 2y + 6z = b2 and –2x – y – 3z = b3
- –x + 2y – 5z = b1, 2x – 4y + 10z = b2 and x – 2y + 5z = b3
- x + 2y + 5z = b1, 2x + 3z = b2 and x + 4y – 5z = b3
Answer
(D) x + 2 y + 5 z = b 1 , 2 x + 3 z = b 2 and x + 4 y – 5 z = b 3
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