KCET · Maths · Indefinite Integration
The symmetric part of the matrix \( A=\left(\begin{array}{ccc}1 & 2 & 4 \\ 6 & 8 & 2 \\ 2 & -2 & 7\end{array}\right) \) is
- A \( \left(\begin{array}{lll}1 & 4 & 3 \\ 2 & 8 & 0 \\ 3 & 0 & 7\end{array}\right) \)
- B \( \left(\begin{array}{lll}1 & 4 & 3 \\ 4 & 8 & 0 \\ 3 & 0 & 7\end{array}\right) \)
- C \( \left(\begin{array}{ccc}0 & -2 & -1 \\ -2 & 0 & -2 \\ -1 & -2 & 0\end{array}\right) \)
- D \( \left(\begin{array}{ccc}0 & -2 & 1 \\ 2 & 0 & 2 \\ -1 & 2 & 0\end{array}\right) \)
Answer & Solution
Correct Answer
(B) \( \left(\begin{array}{lll}1 & 4 & 3 \\ 4 & 8 & 0 \\ 3 & 0 & 7\end{array}\right) \)
Step-by-step Solution
Detailed explanation
Given that \( A=\left[\begin{array}{ccc}1 & 2 & 4 \\ 6 & 8 & 2 \\ 2 & -2 & 7\end{array}\right] \)
Symmetric part of A matrix is \( \frac{1}{2}\left(A+A^{\prime}\right) \)
\( =\frac{1}{2}\left[\begin{array}{ccc}1 & 2 & 4 \\ 6 & 8 & 2 \\ 2 & -2 & 7\end{array}\right]+\left[\begin{array}{ccc}1 & 6 & 2 \\ 2 & 8 & -2 \\ 4 & 2 & 7\end{array}\right] \)
\( =\left[\begin{array}{lll}1 & 4 & 3 \\ 4 & 8 & 0 \\ 3 & 0 & 7\end{array}\right] \)
Symmetric part of A matrix is \( \frac{1}{2}\left(A+A^{\prime}\right) \)
\( =\frac{1}{2}\left[\begin{array}{ccc}1 & 2 & 4 \\ 6 & 8 & 2 \\ 2 & -2 & 7\end{array}\right]+\left[\begin{array}{ccc}1 & 6 & 2 \\ 2 & 8 & -2 \\ 4 & 2 & 7\end{array}\right] \)
\( =\left[\begin{array}{lll}1 & 4 & 3 \\ 4 & 8 & 0 \\ 3 & 0 & 7\end{array}\right] \)
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