Vector Algebra ...

If \(2\left[\begin{array}{ll}1 & 3 \\ 0 & x \end{array}\right]+\left[\begin{array}{ll} y & 0 \\ 1 & 2\end{array}\right]=\left[\begin{array}{ll}5 & 6 \\ 1 & 8\end{array}\right]\) then find the value of \(x+y\).

If \(\left[\begin{array}{cc}2 x+y & 4 x \\ 5 x-7 & 4 x\end{array}\right]=\left[\begin{array}{cc}7 & 7 y-13 \\ y & x+6\end{array}\right]\), then \(x+y=?\)

If \(A =\left[\begin{array}{ll}1 & 2 \\ 1 & 1\end{array}\right]\) and \(B =\left[\begin{array}{cc}0 & -1 \\ 1 & 2\end{array}\right]\), then \(B ^{-1} A ^{-1}\) is equal to:

If \(A=\left[\begin{array}{cc}4 & -3 \\ 1 & 0\end{array}\right]\) then \(A+A^{T}\) is equal to:

Construct a \(3 \times 2\) matrix whose elements are given by \(a _{ ij }=\frac{1}{3}|2 i + j |\).

If \(A=\left(\begin{array}{lll}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{array}\right)\), then \(A^{-1}=\) ?

If \(A B^{T}\) is defined as a square matrix then what is the order of the matrix \(B\), where matrix \(A\) has order \(2 \times 3\)?

If \(A=\left[\begin{array}{cc}\sin \alpha & -\cos \alpha \\ \cos \alpha & \sin \alpha\end{array}\right]\), then for what value of \(\alpha, A\) is an identity matrix?

If \(A=\left[\begin{array}{cc}2 & 3 \\ -1 & 2\end{array}\right]=\frac{1}{2}(P+Q)\) where \(P\) is symmetric and \(Q\) is skew symmetric matrix then \(P\) and \(Q\) are:

If \(A=\left[\begin{array}{cc}1 & -1 \\ -1 & 1\end{array}\right]\), then the expression \(A^3-2 A^2\) is: