यदि A = [(2, -1), (3, 2)] और B = [(0, 4), (-1, 7)] ​तो 3A^2 - 2B ज्ञात करें।

Question

यदि \(\mathrm{A}=\left[\begin{array}{cc}2 & -1 \\ 3 & 2\end{array}\right]\) और \(\mathrm{B}=\left[\begin{array}{cc}0 & 4 \\ -1 & 7\end{array}\right]\) तो \(3 A^{2}-2 B\) ज्ञात करें।

Answer 1

\(\mathrm{A.A}=\left[\begin{array}{cc}2 & -1 \\ 3 & 2\end{array}\right] \left[\begin{array}{cc}2 & -1 \\ 3 & 2\end{array}\right] \)

\(= \left[\begin{array}{cc}4 -3 & -2 -2 \\ 6+6 & -3 +4\end{array}\right] \)

\(= \left[\begin{array}{cc}1 & -4 \\ 12 & 1\end{array}\right] \)

\(3 A^{2}-2 B=3\left[\begin{array}{cc}1 & -4 \\ 12 & 1\end{array}\right]-2\left[\begin{array}{cc}0 & 4 \\ -1 & 7\end{array}\right]\)

\(=\left[\begin{array}{cc}3 & -12 \\ 36 & 3\end{array}\right]-\left[\begin{array}{cc}0 & 8 \\ -2 & 14\end{array}\right]\)

\(=\left[\begin{array}{cc}3 & -20 \\ 40 & -10\end{array}\right]\)