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Mathematics Test - 27
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  • Question 1/10
    5 / -1

    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?

  • Question 2/10
    5 / -1

    The given matrices are:

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

  • Question 3/10
    5 / -1
    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?
  • Question 4/10
    5 / -1
    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.
  • Question 5/10
    5 / -1
    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?
  • Question 6/10
    5 / -1
    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 
  • Question 7/10
    5 / -1

    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

  • Question 8/10
    5 / -1
    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?
  • Question 9/10
    5 / -1
    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?
  • Question 10/10
    5 / -1
    If A, B are square matrices of the same order and B is a skew-symmetric matrix, then A′BA is:
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