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JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the system of linear equations \(x_1 + 2x_2 + 3x_3 = 6\) ; \(x_1 + 3x_2 + 5x_3 = 9\) ; \(2x_1 + 5x_2 + ax_3 = b\) is consistent and has infinite number of solutions, then
- A \(a = 8,\,b\) can be any real number
- B \(b = 15,\,a\) can be any real number
- C \(a \in R - \{8\}\) and \(b \in R- \{15\}\)
- D \(a = 8,\,b = 15\)
Answer & Solution
Correct Answer
(D) \(a = 8,\,b = 15\)
Step-by-step Solution
Detailed explanation
Given system of equations can written in matrix form as \(AX=B\) where \(A = \left( {\begin{array}{*{20}{c}} 1&2&3\\ 1&3&5\\ 2&5&a \end{array}} \right)\) and \(B = \left( {\begin{array}{*{20}{c}} 6\\ 9\\ b \end{array}} \right)\) Since, system is consistent and has infonitely…
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