Mathematics Tes...

Consider the following statements:

1. Every zero matrix is a square matrix.

2. A matrix has a numerical value.

3. A unit matrix is a diagonal matrix.

Which of the above statements is / are correct?

The given matrices are:

\(A = \left[ {\begin{array}{*{20}{c}} {\sqrt 2 }&0&0\\ 0&{\sqrt 2 }&0\\ 0&0&{\sqrt 2 } \end{array}} \right],B = \left[ {\begin{array}{*{20}{c}} 2&0&0\\ 0&1&0\\ 0&0&{ - 5} \end{array}} \right]\)

If \(A = \left[ {\begin{array}{*{20}{c}} {\sin\alpha }&{ - \cos \alpha }\\ {\cos\alpha }&{\sin \alpha } \end{array}} \right]\), then for what value of α, A is an identity matrix?

If A \(= \;\left[ {\begin{array}{*{20}{c}} 1&{ 1}\\ 4&{ 6} \end{array}} \right]\) , find k so that \({A^2} = kA - 2I\), where I is an identity matrix.

If the matrix \(A=\begin{bmatrix}2-x&1&1\\\ 1&3-x&0\\\ -1&-3&-x\end{bmatrix}\) is singular, then what is the solution set S?

If A is a symmetric matrix and B is a skew-symmetric matrix such that A + B = \(\left[ {\begin{array}{*{20}{c}} 2&3\\ 5&{ - 1} \end{array}} \right]\), then AB is equal to 

Which of the following statements is/are true

If A and B are two skew-symmetric matrices of order n then

1. A ⋅ B is a skew symmetric matrix when AB = - BA

2. A ⋅ B is a symmetric matrix when AB = BA

If A = \(\left[ {\begin{array}{*{20}{c}} 1&{3 + x}&2\\ {1 - x}&2&{y + 1}\\ 2&{5 - y}&3 \end{array}} \right]\) is a symmetric matrix, then 3x + y is equal to?

If \(\rm A=\begin{bmatrix} x & 2 \\\ 4 & 3 \end{bmatrix}\) and \(\rm A ^{-1}=\begin{bmatrix} {1\over8} & {-1\over 12} \\\ {-1\over 6}& {4\over 9} \end{bmatrix}\), then find the value of x?

If A, B are square matrices of the same order and B is a skew-symmetric matrix, then A′BA is: