Vector Algebra ...

If \(A=\left[\begin{array}{ccc}2 & x-3 & x-2 \\ 3 & -2 & -1 \\ 4 & -1 & -5\end{array}\right]\) is a symmetric matrix then \(x=?\)

Find the value of \(X\) and \(Y\) if \(X+Y=\left[\begin{array}{cc}10 & 2 \\ 0 & 9\end{array}\right], X-Y=\left[\begin{array}{cc}6 & 12 \\ 0 & -5\end{array}\right]\).

Consider the matrix \(A=\left[\begin{array}{ccc}2 & 4 & 5 \\ 1 & 6 & 4 \\ 2 & 8 & 9\end{array}\right]\). Find the element:

What is the order of \(\left[\begin{array}{lll}4 & 4 & 1\end{array}\right]\left[\begin{array}{lll}3 & 2 & 5 \\ 9 & 7 & 4 \\ 6 & 4 & 1\end{array}\right]\) ?

For \(A=\left[\begin{array}{ll}2 & 4 \\ 0 & 3\end{array}\right]\), then \(A^{-1}\) is given by :

Order of \(\left[\begin{array}{lll}2 & 7 & 4 \\ 3 & 1 & 0\end{array}\right]\left[\begin{array}{l}5 \\ 4 \\ 3\end{array}\right]\) is:

If \(A =\left[\begin{array}{cc}4 & x +2 \\ 2 x -3 & x +1\end{array}\right]\) is symmetric, then \(x\) is equal to:

If \(A =\left[\begin{array}{rr}0 & - i \\ i & 0\end{array}\right]\) and \(B =\left[\begin{array}{rr}1 & 0 \\ 0 & -1\end{array}\right]\) are matrices, then \(AB + BA\) is:

If \(A =\left[\begin{array}{ccc}1 & -1 & 0 \\ 3 & 2 & -1\end{array}\right]\) and \(B =\left[\begin{array}{l}1 \\ 3 \\ 5\end{array}\right]\), find \(( AB )^{T}\).

If \(\left[\begin{array}{ccc}1 & -3 & 2 \\ 2 & -8 & 5 \\ 4 & 2 & \lambda\end{array}\right]\) is not an invertible matrix, then what is the value of \(\lambda\)?