Worksheet: Transpose of a Matrix

Practice

In this worksheet, we will practice finding the transpose of a matrix, elements of a given row and column after transposing, and a matrix's dimensions after transposing.

Q1:

Find the transpose of the matrix − 5 4 4 .

  • A ( 4 4 − 5 )
  • B ( 5 − 4 − 4 )
  • C 4 4 − 5
  • D ( − 5 4 4 )

Q2:

If 𝐴 = 6 7 and 𝐵 = ( 5 0 ) , what is ( 𝐵 𝐴 ) 𝑇 ?

  • A 3 0 4 2 0 1 4
  • B ( − 3 0 )
  • C 3 0 0 4 2 1 4
  • D ( 3 0 )

Q3:

Given that what is 𝐴 𝐵 𝑇 𝑇 ?

  • A − 5 − 7 − 4 8
  • B 8 − 4 − 7 − 5
  • C − 5 − 4 − 7 8
  • D 8 − 7 − 4 − 5

Q4:

Given the matrix find 𝐴 𝑇 𝑇 .

  • A − 8 4 4 1 3 − 1
  • B − 8 4 4 1 3 − 1
  • C − 8 4 3 4 1 − 1
  • D − 8 4 3 4 1 − 1

Q5:

Consider the matrices Is it true that ( 𝐶 𝐵 𝐴 ) = 𝐴 𝐵 𝐶 ?

  • AYes
  • BNo

Q6:

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

Q7:

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

  • A 4 × 4
  • B 1 × 1
  • C 4 × 1
  • D 1 × 4

Q8:

Given that determine the value of 𝑎 + 𝑎 1 2 2 1 .

  • A20
  • B8
  • C − 2 0
  • D0

Q9:

Given the shown matrices, determine whether ( 𝑌 − 𝑋 ) = ( 𝑌 ) − ( 𝑋 ) 𝑇 𝑇 𝑇 .

  • Ayes
  • Bno

Q10:

Find the transpose of the matrix 6 − 5 6 1 6 8 .

  • A 6 8 − 5 6 6 1
  • B 1 6 6 − 5 8 6
  • C 1 6 8 6 − 5 6
  • D 6 1 − 5 6 6 8

Q11:

Find the transpose of the matrix 3 5 − 6 − 8 − 5 − 2 .

  • A − 5 − 6 3 − 2 − 8 5
  • B 5 − 8 − 2 3 − 6 − 5
  • C 5 3 − 8 − 6 − 2 − 5
  • D 3 − 6 − 5 5 − 8 − 2

Q12:

Find the transpose of the matrix − 2 − 1 8 .

  • A ( 8 − 1 − 2 )
  • B ( 2 1 − 8 )
  • C 8 − 1 − 2
  • D ( − 2 − 1 8 )

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