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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Matrices

NDA 2019 · Mathematics · Matrices

If B=[ array lll 3 & 2 & 0 2 & 4 & 0 1 & 1 & 0 array ] , then what...

If B=\left[320240110\begin{array}{lll}3 & 2 & 0 \\ 2 & 4 & 0 \\ 1 & 1 & 0\end{array}\right], then what is adjoint of BB equal to?

Options

  1. A\left[000000−2−18\begin{array}{ccc}0 & 0 & 0 \\ 0 & 0 & 0 \\ -2 & -1 & 8\end{array}\right]
  2. B\left[00−200−1008\begin{array}{ccc}0 & 0 & -2 \\ 0 & 0 & -1 \\ 0 & 0 & 8\end{array}\right]
  3. C\left[002001000\begin{array}{lll}0 & 0 & 2 \\ 0 & 0 & 1 \\ 0 & 0 & 0\end{array}\right]
  4. DIt does not exist

Correct answer

A. \left[000000−2−18\begin{array}{ccc}0 & 0 & 0 \\ 0 & 0 & 0 \\ -2 & -1 & 8\end{array}\right]

Step-by-step solution

B=\left[320240110\begin{array}{lll}3 & 2 & 0 \\ 2 & 4 & 0 \\ 1 & 1 & 0\end{array}\right]CfactormatrixofC factor matrix ofB=[(4)(0)−(0)(1)−[(2)(0)−(0)(1)](2)(1)−(4)(1)−[2(0)−(0)(1)]3(0)−(0)(1)−[(3)(1)−(2)(1)]2(0)−0(4)−[3(0)−2(0)]3(4)−2(2)]=[00−200−1008]Adjoint B=[000000−2−18]\begin{aligned} & B=\left[\begin{array}{ccc}(4)(0)-(0)(1) & -[(2)(0)-(0)(1)] & (2)(1)-(4)(1) \\ -[2(0)-(0)(1)] & 3(0)-(0)(1) & -[(3)(1)-(2)(1)] \\ 2(0)-0(4) & -[3(0)-2(0)] & 3(4)-2(2)\end{array}\right] \\ & =\left[\begin{array}{ccc}0 & 0 & -2 \\ 0 & 0 & -1 \\ 0 & 0 & 8\end{array}\right] \\ & \text{Adjoint } B=\left[\begin{array}{ccc}0 & 0 & 0 \\ 0 & 0 & 0 \\ -2 & -1 & 8\end{array}\right]\end{aligned}$
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