AP EAMCET · Maths · Matrices
The values of \(p\) and \(q\) so that the system of equations \(2 x+p y+6 z=8\), \(x+2 y+q z=5\) and \(x+y+3 z=4\) may have no solution are
- A \(p \neq 2, q=3\)
- B \(p \neq 2, q \neq 3\)
- C \(p=2, q=\frac{15}{4}\)
- D \(p=2, q=3\)
Answer & Solution
Correct Answer
(A) \(p \neq 2, q=3\)
Step-by-step Solution
Detailed explanation
\(\begin{pmatrix} 2 & p & 6 & 8 \\ 1 & 2 & q & 5 \\ 1 & 1 & 3 & 4 \end{pmatrix}\) \(R_1 \leftrightarrow R_3 \Rightarrow \begin{pmatrix} 1 & 1 & 3 & 4 \\ 1 & 2 & q & 5 \\ 2 & p & 6 & 8 \end{pmatrix}\) \(R_2 \leftarrow R_2 - R_1\),…
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