Matrices Test -...

If \(A=\left[\begin{array}{cc}\cos 2 \theta & -\sin 2 \theta \\ \sin 2 \theta & \cos 2 \theta\end{array}\right]\) and \(A + A ^{T}= I\) Where \(I\) is the unit matrix of \(2 \times 2\) and  \(A ^{T}\) is the transpose of \(A\), then the value of \(\theta\) is equal to:

Consider the following statements in respect of the matrix \(A=\left[\begin{array}{ccc}0 & 1 & 2 \\ -1 & 0 & -3 \\ -2 & 3 & 0\end{array}\right]\)

1) The matrix \(A\) is skew-symmetric.

2) The matrix \(A\) is symmetric.

3) The matrix \(A\) is Iinvertible.

Which of the above statements is/are correct?

If \(\left[\begin{array}{ccc}1 & -4 & 3 \\ 0 & 6 & -7 \\ 2 & 4 & \lambda\end{array}\right]\) is not an invertible matrix, then what is the value of \(\lambda\)?

If \(x+2 y=\left[\begin{array}{cc}2 & -3 \\ 1 & 5\end{array}\right]\) and \(2 x+5 y=\left[\begin{array}{ll}7 & 5 \\ 2 & 3\end{array}\right]\), then \(y\) is equal to:

If \(A=\left[\begin{array}{ccc}1 & 3+x & 2 \\ 1-x & 2 & y+1 \\ 2 & 5-y & 3\end{array}\right]\) is a symmetric matrix, then \(3 x+y\) is equal to:

The inverse of the matrix \(\left[\begin{array}{ccc}2 & 5 & 0 \\ 0 & 1 & 1 \\ -1 & 0 & 3\end{array}\right]\) is:

Find the value of \(x\) and \(y\) such that \(\left[\begin{array}{l}x-y \\ x+y\end{array}\right]=\left[\begin{array}{c}2 \\ 16\end{array}\right]\).

If \(A =\left[\begin{array}{cc}\cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha\end{array}\right]\) then \(AA ^{T}\) is equal to: (where \(A ^{ T }\) is the transpose of \(\left.A \right)\)

Find \(2 X-Y\) matrix such as \(X+Y=\left[\begin{array}{ll}7 & 5 \\ 3 & 4\end{array}\right]\) and \(X-Y=\left[\begin{array}{cc}1 & -3 \\ 3 & 0\end{array}\right]\).

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 \(A B^{T}\) 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 \(A =\left[\begin{array}{cc}1 & -5 \\ -3 & 7\end{array}\right]\) and \(B =\left[\begin{array}{ll}8 & 4 \\ 1 & 3\end{array}\right]\) then the value of \(( AB )^{T}\) is:

If matrix \(A =\left[\begin{array}{cc}1 & -2 \\ -6 & 4\end{array}\right]\) and \(B =\left[\begin{array}{cc}2 & -1 \\ 1 & 3\end{array}\right]\), that \(A \left( B ^{ T }\right)\) is:

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 the inverse of the matrix \(A=\left[\begin{array}{lll}3 & 1 & 2 \\ 4 & 2 & 1 \\ 2 & a & 1\end{array}\right]\) does not exist then the value of a is:

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

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 \(x\):

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

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 \(\lambda\)?