TS EAMCET · Maths · Matrices
If the system of simultaneous linear equations \(x-2 y+z=0,2 x+3 y+z=6\) and \(x+2 y+p z=q\) has infinitely many solutions, then
- A \(p+q=4\)
- B \(p q=\frac{48}{49}\)
- C \(q-p=3\)
- D \(\frac{p}{q}=4\)
Answer & Solution
Correct Answer
(C) \(q-p=3\)
Step-by-step Solution
Detailed explanation
\(D = \begin{vmatrix} 1 & -2 & 1 \\ 2 & 3 & 1 \\ 1 & 2 & p \end{vmatrix} = 0\) \(1(3p-2) - (-2)(2p-1) + 1(4-3) = 0\) \(3p-2 + 4p-2 + 1 = 0\) \(7p-3 = 0 \Rightarrow p = \frac{3}{7}\) \(D_z = \begin{vmatrix} 1 & -2 & 0 \\ 2 & 3 & 6 \\ 1 & 2 & q \end{vmatrix} = 0\)…
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