यदि 2A + B + X = 0, जहाँ A = [{-1, 2}, {3, 4}] और B = [{3, -2}, {1, 5}] तो X =

Question

यदि \(2 A+B+X=0\), जहाँ \(A=\left[\begin{array}{rr}-1 & 2 \\ 3 & 4\end{array}\right]\) और \(B=\left[\begin{array}{rr}3 & -2 \\ 1 & 5\end{array}\right]\) तो \(X=\)

(A) \(\left[\begin{array}{rr}1 & 2 \\ -7 & -13\end{array}\right]\)

(B) \(\left[\begin{array}{cc}1 & 2 \\ 7 & 13\end{array}\right]\)

(C) \(\left[\begin{array}{cc}-1 & -2 \\ -7 & -13\end{array}\right]\)

(D) \(\left[\begin{array}{rr}-1 & -2 \\ 7 & 13\end{array}\right]\)

Answer 1

सही विकल्प है (C) \(\left[\begin{array}{cc}-1 & -2 \\ -7 & -13\end{array}\right]\)

\(2 A+B+X=0\)

\(X = -2A - B\)

\(X = -2 \begin{bmatrix} - 1&2\\3&4\end{bmatrix} - \begin{bmatrix} 3& -2\\1& 5\end{bmatrix}\)

\(= \begin{bmatrix} 2&-4\\-6&-8\end{bmatrix} - \begin{bmatrix} 3& -2\\1& 5\end{bmatrix}\)

\(= \begin{bmatrix} 2-3&-4 + 2\\-6 - 1&-8 -5\end{bmatrix} \)

\(=\left[\begin{array}{cc}-1 & -2 \\ -7 & -13\end{array}\right]\)