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Lesson: Transpose of a Matrix

Worksheet • 12 Questions

Q1:

What operation must be performed on the matrix to get the matrix ? How does this operation affect the value of the determinant?

  • AThe second matrix is the transpose of the first. The determinant of the second matrix is the same as the determinant of the first matrix.
  • BThe second matrix is the inverse of the first. The determinant of the second matrix is the same as the determinant of the first matrix.
  • CThe second matrix is the inverse of the first. The determinant of the second matrix is the reciprocal of the determinant of the first matrix.
  • DThe second matrix is the first matrix with the rows swapped. The determinant of the second matrix is times the determinant of the first matrix.
  • EThe second matrix is the first matrix with the columns swapped. The determinant of the second matrix is times the determinant of the first matrix.

Q2:

Consider the matrices Is it true that ( 𝐢 𝐡 𝐴 ) = 𝐴 𝐡 𝐢     ?

  • ANo
  • BYes

Q3:

If 𝑋 is a matrix of order 4 Γ— 1 , then what is the order of the matrix 𝑋 𝑇 ?

  • A 1 Γ— 4
  • B 1 Γ— 1
  • C 4 Γ— 1
  • D 4 Γ— 4

Q4:

If 𝐴 = ο€Ό 6 7  and 𝐡 = ( 5 0 ) , what is ( 𝐡 𝐴 ) 𝑇 ?

  • A ( 3 0 )
  • B ( βˆ’ 3 0 )
  • C ο€Ό 3 0 0 4 2 1 4 
  • D ο€Ό 3 0 4 2 0 1 4 

Q5:

Given that what is 𝐴 𝐡 𝑇 𝑇 ?

  • A ο€Ό 8 βˆ’ 7 βˆ’ 4 βˆ’ 5 
  • B ο€Ό 8 βˆ’ 4 βˆ’ 7 βˆ’ 5 
  • C ο€Ό βˆ’ 5 βˆ’ 4 βˆ’ 7 8 
  • D ο€Ό βˆ’ 5 βˆ’ 7 βˆ’ 4 8 

Q6:

Given that determine the value of π‘Ž + π‘Ž 1 2 2 1 .

  • A0
  • B8
  • C βˆ’ 2 0
  • D20

Q7:

Find the transpose of the matrix  βˆ’ 5 4 4  .

  • A ( βˆ’ 5 4 4 )
  • B ( 5 βˆ’ 4 βˆ’ 4 )
  • C  4 4 βˆ’ 5 
  • D ( 4 4 βˆ’ 5 )

Q8:

Find the transpose of the matrix ο€Ό 6 βˆ’ 5 6 1 6 8  .

  • A  6 1 βˆ’ 5 6 6 8 
  • B  1 6 6 βˆ’ 5 8 6 
  • C ο€Ό 1 6 8 6 βˆ’ 5 6 
  • D  6 8 βˆ’ 5 6 6 1 

Q9:

Find the transpose of the matrix  3 5 βˆ’ 6 βˆ’ 8 βˆ’ 5 βˆ’ 2  .

  • A ο€Ό 3 βˆ’ 6 βˆ’ 5 5 βˆ’ 8 βˆ’ 2 
  • B ο€Ό 5 βˆ’ 8 βˆ’ 2 3 βˆ’ 6 βˆ’ 5 
  • C  5 3 βˆ’ 8 βˆ’ 6 βˆ’ 2 βˆ’ 5 
  • D ο€Ό βˆ’ 5 βˆ’ 6 3 βˆ’ 2 βˆ’ 8 5 

Q10:

Find the transpose of the matrix  βˆ’ 2 βˆ’ 1 8  .

  • A ( βˆ’ 2 βˆ’ 1 8 )
  • B ( 2 1 βˆ’ 8 )
  • C  8 βˆ’ 1 βˆ’ 2 
  • D ( 8 βˆ’ 1 βˆ’ 2 )

Q11:

Given the matrix find ο€Ή 𝐴  𝑇 𝑇 .

  • A ο€Ό βˆ’ 8 4 3 4 1 βˆ’ 1 
  • B  βˆ’ 8 4 4 1 3 βˆ’ 1 
  • C  βˆ’ 8 4 3 4 1 βˆ’ 1 
  • D ο€Ό βˆ’ 8 4 4 1 3 βˆ’ 1 

Q12:

Given the shown matrices, determine whether ( π‘Œ βˆ’ 𝑋 ) = ( π‘Œ ) βˆ’ ( 𝑋 ) 𝑇 𝑇 𝑇 .

  • Ano
  • Byes
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