Math MCQs of Matrices . (for board classes)

Math MCQs of Matrices

  Let \(A= \begin{bmatrix} 5 &0 \\ 0 & 6 \end{bmatrix}\) then \(A\) is?

  symmetric matrix
  skew-symmetric matrix
  scalene matrix
  nilpotent matrix

Answer

Answer:symmetric matrix

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  If \(A=\begin{bmatrix} \cos x & -\sin x\\ \sin x& \cos x \end{bmatrix}\) ,then \(A.A^{t}\) is ?

  Zero matrix

  \(\begin{bmatrix} 1 &1 \\ 0& 1 \end{bmatrix}\)

  \(\begin{bmatrix} 1 &0 \\ 0& 1 \end{bmatrix}\)

  None of these

Answer

Answer:\(\begin{bmatrix} 1 &0 \\ 0& 1 \end{bmatrix}\)

HINT- use the properties of orthogonal matrix (here A is orthogonal you can check)

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  If \(A\) is a \(3 \times 3\) matrix such that \(| A |=3\), then \(|adj A|\) is ?

  \(81\)
  \(3\)
  \(27\)
  \(9\)

Answer

Answer:9

because \(|adj (A))| = |A|^{n-1}\) where \(n\) is order of matrix

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  Let \(A= \begin{bmatrix} 2 &0 \\ 0 & 5 \end{bmatrix}\) then \(A^{-1}\) is?

  \(\begin{bmatrix} 3 &0 \\ 0& 1 \end{bmatrix}\)

  \(\begin{bmatrix} 1 &0 \\ 0& 1 \end{bmatrix}\)

  \(\begin{bmatrix} \frac{1}{2} &0 \\ 0& \frac{1}{5} \end{bmatrix}\)

  \(\begin{bmatrix} \frac{1}{2} &0 \\ 0& -\frac{1}{5} \end{bmatrix}\)

Answer

Answer: \(\begin{bmatrix} \frac{1}{2} &0 \\ 0& \frac{1}{5} \end{bmatrix}\)

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  Let \(A=\begin{pmatrix} 2x & 0\\ x& x \end{pmatrix}\) and \(A^{-1}=\begin{pmatrix} 1 &0 \\ -1& 2 \end{pmatrix}\) then \(x\) is equal to ?

  \(2\)
  \(-1/2\)
  \(-1\)
  \( 1/2\)

Answer

Answer:\(1/2\)

HINT- use rule \(A.A^{-1}=I\)

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  If \(A^2-A+I=0\), then \(A^{-1}=?\)

  \(A\)
  \(-A\)
  \(I-A\)
  \(A+I\)

Answer

Answer:\(I-A\)

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  If \(A=\begin{bmatrix} 1& x & y\\ 2 & 0 & 4\\ -1& z & 0 \end{bmatrix}\) is symmetrix matrix then \(x,y,z\) is ?

  \(1,2,4\)
  \(2,-1,4\)
  \( 2,2,2 \)
  \( -2,1,-4\)

Answer

Answer:\(2,-1,4\)

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  For any square matrix \(A, A.A^{T}\) is a ?

  unit matrix
  symmetric matrix
  skew-symmetric matrix
  diagonal matrix

Answer

Answer:symmetric matrix

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  If \(A^{2}=I\),then \((A-I)^3+3A^{2}\)= ?

  \(I_{3}\)
  \(3A-3A^{2}\)
  \(4A\)
  \(3A\)

Answer

Answer:\(3A\)

HINT-Expand \((A-I)^3\)

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  Total number of possible matrices of order \(3 \times 3\) with each entry 2 or 0 is ?

  \(9\)
  \(27\)
  \(512\)
  \(81\)

Answer

Answer:512 ?

HINT- total number of places in order 3 matirx is 9, and you can fill 0 or 2 on any place so total possabilites are \(2^9\)

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