TS EAMCET · Maths · Determinants
If \(\Delta=\left|\begin{array}{lll}1 & 5 & 6 \\ 0 & 1 & 7 \\ 0 & 0 & 1\end{array}\right|\) and \(\Delta^{\prime}=\left|\begin{array}{ccc}1 & 0 & 1 \\ 3 & 0 & 3 \\ 4 & 6 & 100\end{array}\right|\), then
- A \(\Delta^2-3 \Delta^{\prime}=0\)
- B \(\left(\Delta+\Delta^{\prime}\right)^2-3\left(\Delta+\Delta^{\prime}\right)+2=0\)
- C \(\left(\Delta+\Delta^{\prime}\right)^2+3\left(\Delta+\Delta^{\prime}\right)+5=0\)
- D \(\Delta+3 \Delta^{\prime}+1=0\)
Answer & Solution
Correct Answer
(B) \(\left(\Delta+\Delta^{\prime}\right)^2-3\left(\Delta+\Delta^{\prime}\right)+2=0\)
Step-by-step Solution
Detailed explanation
Given, \[ \begin{aligned} \Delta & =\left|\begin{array}{lll} 1 & 5 & 6 \\ 0 & 1 & 7 \\ 0 & 0 & 1 \end{array}\right| \\ & =1(1-0)-5(0-0)+6(0-0) \\ & =1-0+0 \end{aligned} \] \[ \Rightarrow \quad \Delta=1 \] If \(\Delta=1\) and…
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