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Lesson: Adjoint Matrix

Worksheet • 6 Questions

Q1:

Complete the following statement: a linear operator 𝐴 ∢ ℝ β†’ ℝ   is self-adjoint if and only of it is .

  • Asymmetric
  • Bbounded
  • Cnormal
  • Dcontinuous

Q2:

Find the adjoint matrix of the matrix

  • A  7 3 βˆ’ 1 8 7 7 3 6 8 0 βˆ’ 1 0 1 4 6 βˆ’ 7 7 
  • B  7 3 1 8 7 7 βˆ’ 3 6 8 0 βˆ’ 1 0 1 βˆ’ 4 6 βˆ’ 7 7 
  • C  7 3 3 6 βˆ’ 1 0 1 βˆ’ 1 8 8 4 6 7 7 0 βˆ’ 7 7 
  • D  2 7 2 9 βˆ’ 7 9 βˆ’ 8 βˆ’ 5 βˆ’ 4 

Q3:

Find the adjoint matrix of the matrix

  • A  1 6 βˆ’ 3 3 βˆ’ 9 βˆ’ 5 7 2 7 4 5 βˆ’ 3 0 3 6 βˆ’ 9 
  • B  1 6 3 3 βˆ’ 9 5 7 2 7 βˆ’ 4 5 βˆ’ 3 0 βˆ’ 3 6 βˆ’ 9 
  • C  1 6 βˆ’ 5 7 βˆ’ 3 0 βˆ’ 3 3 2 7 3 6 βˆ’ 9 4 5 βˆ’ 9 
  • D  βˆ’ 9 3 βˆ’ 6 9 βˆ’ 2 1 βˆ’ 6 βˆ’ 2 βˆ’ 7 

Q4:

Find the adjoint matrix of the matrix

  • A  3 6 1 5 3 1 0 0 3 0 1 1 1 7 6 6 9 2 
  • B  3 6 βˆ’ 1 5 3 1 0 0 βˆ’ 3 0 1 1 1 βˆ’ 7 6 6 βˆ’ 9 2 
  • C  3 6 3 0 6 1 5 3 1 1 1 9 1 0 0 7 6 2 
  • D  βˆ’ 7 βˆ’ 9 8 βˆ’ 6 βˆ’ 8 βˆ’ 4 βˆ’ 6 βˆ’ 9 βˆ’ 9 

Q5:

Find the adjoint matrix of the matrix

  • A  βˆ’ 6 5 5 9 2 0 1 0 βˆ’ 6 2 βˆ’ 5 6 βˆ’ 1 0 1 7 8 4 
  • B  βˆ’ 6 5 βˆ’ 5 9 2 0 βˆ’ 1 0 βˆ’ 6 2 5 6 βˆ’ 1 0 1 βˆ’ 7 8 4 
  • C  βˆ’ 6 5 1 0 βˆ’ 1 0 1 5 9 βˆ’ 6 2 7 2 0 βˆ’ 5 6 8 4 
  • D  βˆ’ 7 7 βˆ’ 3 βˆ’ 7 βˆ’ 5 5 βˆ’ 9 8 5 

Q6:

Find the adjoint matrix of the matrix

  • A  βˆ’ 8 1 7 2 4 βˆ’ 7 βˆ’ 4 2 1 4 9 2 8 4 
  • B  βˆ’ 8 βˆ’ 1 7 2 4 7 βˆ’ 4 βˆ’ 2 1 4 9 βˆ’ 2 8 4 
  • C  βˆ’ 8 βˆ’ 7 4 9 1 7 βˆ’ 4 2 8 2 4 2 1 4 
  • D  βˆ’ 4 βˆ’ 4 3 βˆ’ 7 βˆ’ 8 0 0 βˆ’ 7 1 
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