TS EAMCET · Maths · Determinants
If \(A X=D\) represents the system of linear equations \(3 x-4 y+7 z+6=0,5 x+2 y-4 z+9=0\) and \(8 x-6 y-z+5=0\), then
- A \(\operatorname{Rank}(A)=\operatorname{Rank}([A D])=1\)
- B \(\operatorname{Rank}(A)=\operatorname{Rank}([A D])=2\)
- C \(\operatorname{Rank}(A)=\operatorname{Rank}([A D])=3\)
- D \(\operatorname{Rank}\neq \operatorname{Rank}([A D])\)
Answer & Solution
Correct Answer
(C) \(\operatorname{Rank}(A)=\operatorname{Rank}([A D])=3\)
Step-by-step Solution
Detailed explanation
Here \(A=\left[\begin{array}{ccc}3 & -4 & 7 \\ 5 & 2 & -4 \\ 8 & -6 & -1\end{array}\right] ; \quad|A|=\left|\begin{array}{ccc}3 & -4 & 7 \\ 5 & 2 & -4 \\ 8 & -6 & -1\end{array}\right|\)…
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