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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Matrices

NDA 2013 · Mathematics · Matrices

If ( array ll 2 & 3 4 & 1 array ) × ( array cc 5 & -2 -3 & 1 array...

If \left(2341\begin{array}{ll}2 & 3 \\ 4 & 1\end{array}\right) \times \left(\begin{array}{cc}5 & -2 \\ -3 & 1\end{array}$\right)=\left(\begin{array}{cc}1 & -1 \\ 17 & \lambda\end{array}$$\right) then what is λ\lambda equal to?$

Options

  1. A7
  2. B–7
  3. C9
  4. D–9

Correct answer

B. –7

Step-by-step solution

∣2341∣∣5−2−31∣=∣1−117λ∣=∣2×5−3×3−2×2+3×14×5−1×3−4×2+1×1∣=∣1−117λ∣=∣1−117−7∣=∣1−117λ∣∴λ=−7\begin{aligned} & \left|\begin{array}{ll}2 & 3 \\ 4 & 1\end{array}\right|\left|\begin{array}{cc}5 & -2 \\ -3 & 1\end{array}\right|=\left|\begin{array}{cc}1 & -1 \\ 17 & \lambda\end{array}\right| \\ & =\left|\begin{array}{cc}2 \times 5-3 \times 3 & -2 \times 2+3 \times 1 \\ 4 \times 5-1 \times 3 & -4 \times 2+1 \times 1\end{array}\right|=\left|\begin{array}{cc}1 & -1 \\ 17 & \lambda\end{array}\right| \\ & =\left|\begin{array}{cc}1 & -1 \\ 17 & -7\end{array}\right|=\left|\begin{array}{cc}1 & -1 \\ 17 & \lambda\end{array}\right| \\ & \therefore \quad \lambda=-7\end{aligned}
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