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Worksheet: Transpose of a Matrix

Q1:

What operation must be performed on the matrix  π‘Ž 𝑏 𝑐 𝑑  to get the matrix  π‘Ž 𝑐 𝑏 𝑑  ? 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 βˆ’ 1 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 βˆ’ 1 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.

Q2:

Consider the given matrices. Is it true that ?

  • Ayes
  • Bno

Q3:

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

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

Q4:

If and , what is ?

  • A
  • B
  • C
  • D

Q5:

Given that what is ?

  • A
  • B
  • C
  • D

Q6:

Given that determine the value of .

  • A20
  • B8
  • C
  • D0

Q7:

Find the transpose of the matrix .

  • A
  • B
  • C
  • D

Q8:

Find the transpose of the matrix .

  • A
  • B
  • C
  • D

Q9:

Find the transpose of the matrix .

  • A
  • B
  • C
  • D

Q10:

Find the transpose of the matrix .

  • A
  • B
  • C
  • D

Q11:

Give the following matrix, find .

  • A
  • B
  • C
  • D

Q12:

Given the shown matrices, determine whether .

  • Ayes
  • Bno