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Question - 1

The rank of the matrix \(\begin{pmatrix} 1 & -1 & 2 \\ 2 & -2 & 4 \\ 4 & -4 & 8 \end{pmatrix}\) is ?

  • A 1
  • B 2
  • C 3
  • D 4

Question - 2

The rank of the diagonal matrix \(\begin{pmatrix} -1 &0 &0 &0 &0 \\ 0& 2 &0 & 0&0 \\0 &0 & 0 &0 &0 \\ 0& 0& 0& -4 &0 \\0 &0 & 0& 0& 0 \end{pmatrix}\)is

  • A 0
  • B 2
  • C 3
  • D 5

Question - 3

If A = (2 0 1), then the rank of \({ AA }^{ T }\) is ..................

  • A 1
  • B 2
  • C 3
  • D 0

Question - 4

If A = \(\begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}\), then the rank of \({ AA }^{ T }\) is, 

  • A 3
  • B 0
  • C 1
  • D 2

Question - 5

If the rank of the matrix \(\begin{pmatrix} \lambda & -1 & 0 \\ 0 & \lambda & -1 \\ -1 & 0 & \lambda \end{pmatrix}\) is 2, then \(\lambda \) is, 

  • A 1
  • B 2
  • C 3
  • D any real number

Question - 6

If A is a scalar matrix with scalar \(k\neq 0\) , of order 3, then \({ A }^{ -1 }\) is

  • A \(\frac { 1 }{ { k }^{ 2 } } I\)
  • B \(\frac { 1 }{ { k }^{ 3 } } I\)
  • C \(\frac { 1 }{ k } I\)
  • D \(K \ I\)

Question - 7

If the matrix \(\begin{pmatrix} -1 & 3 & 2 \\ 1 & k & -3 \\ 1 & 4 & 5 \end{pmatrix}\)has an inverse then the values of k

  • A k is any real number
  • B k = -4
  • C \(k\neq -4\)
  • D \(k\neq 4\)

Question - 8

If A = \(\begin{pmatrix} 2 & 1 \\ 3 & 4 \end{pmatrix}\), then (adjA) A =

  • A \(\begin{pmatrix} \frac { 1 }{ 5 } & 0 \\ 0 & \frac { 1 }{ 5 } \end{pmatrix}\)
  • B \(\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\)
  • C \(\begin{pmatrix} 5 & 0 \\ 0 & -5 \end{pmatrix}\)
  • D \(\begin{pmatrix} 5 & 0 \\ 0 & 5 \end{pmatrix}\)

Question - 9

If A is a square matrix of order n then \(|adjA|\) is 

  • A \({ |A| }^{ 2 }\)
  • B \({ |A| }^{ n }\)
  • C \({ |A| }^{ n-1 }\)
  • D \(|A|\)

Question - 10

The inverse of the matrix \(\begin{pmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{pmatrix}\) is

  • A \(\begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}\)
  • B \(\begin{pmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ -1 & 0 & 0 \end{pmatrix}\)
  • C \(\begin{pmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{pmatrix}\)
  • D \(\begin{pmatrix} -1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1 \end{pmatrix}\)