Worksheet: Transpose of a Matrix

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In this worksheet, we will practice finding the transpose of a matrix and identifying symmetric and skew-symmetric matrices.

Q1:

Find the transpose of the matrix −544.

  • A [ − 5 4 4 ]
  • B 4 4 − 5
  • C [ 5 − 4 − 4 ]
  • D [ 4 4 − 5 ]

Q2:

Given the matrix 𝐴=−84341−1, find 𝐴.

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

Q3:

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

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

Q4:

Given the matrices 𝑌=−422−7, 𝑋=44−1−7, does (𝑌−𝑋)=𝑌−𝑋?

  • ANo
  • BYes

Q5:

Find the transpose of the matrix −2−18.

  • A [ − 2 − 1 8 ]
  • B 8 − 1 − 2
  • C [ 2 1 − 8 ]
  • D [ 8 − 1 − 2 ]

Q6:

Find the transpose of the matrix 0−81.

  • A [ 0 − 8 1 ]
  • B 1 − 8 0
  • C [ 0 8 − 1 ]
  • D [ 1 − 8 0 ]

Q7:

Find the transpose of the matrix 7−3−2.

  • A [ 7 − 3 − 2 ]
  • B − 2 − 3 7
  • C [ − 7 3 2 ]
  • D [ − 2 − 3 7 ]

Q8:

Which of the following matrices is skew-symmetric?

  • A 3 − 5 − 2 5 − 3 1 2 − 1 3
  • B 0 − 3 − 5 3 0 1 0 5 − 1 0 0
  • C 0 − 1 − 9 1 0 − 6 9 6 7
  • D 1 0 − 9 − 2 − 9 − 2 − 5 − 2 − 5 4

Q9:

Given that the matrix 𝐵=0−2𝑥−63𝑧+1403𝑧−3𝑦+6𝑥−120 is skew-symmetric, find the value of 𝑥+𝑦+𝑧.

Q10:

Find the value of 𝑥 which makes the matrix 𝐴=−15𝑥−3−43−8 symmetric.

Q11:

If 𝐴=−6−2𝑦−𝑦−3𝑥𝑧+5−9𝑧−6−9−2𝑥−11−4 is a symmetric matrix, what are the values of 𝑥, 𝑦, and 𝑧?

  • A 𝑥 = 9 , 𝑦 = − 1 2 , 𝑧 = − 1 7
  • B 𝑥 = 9 , 𝑦 = 0 , 𝑧 = − 1 7
  • C 𝑥 = − 6 , 𝑦 = 0 , 𝑧 = − 5
  • D 𝑥 = 9 , 𝑦 = 0 , 𝑧 = − 5
  • E 𝑥 = − 9 , 𝑦 = 0 , 𝑧 = − 5

Q12:

Which of the following matrices is symmetric?

  • A − 2 3 5 3 − 4 − 3 5 − 3 − 7
  • B − 3 − 5 − 1 − 6 6 5 − 7 7 − 8
  • C − 2 4 − 3 4 − 8 − 8 9 − 3 − 2
  • D − 4 − 4 2 − 4 8 − 2 8 − 2 3

Q13:

Given that 𝐴=𝑎 where 𝑎=3𝑖+5𝑗+9, find the matrix 𝐴. That 𝐴 is 2×3 matrix.

  • A 2 3 2 0 1 7 2 8 2 5 2 3
  • B 2 2 2 5 2 8 1 7 2 0 2 3
  • C 1 7 2 2 2 0 2 5 2 3 2 8
  • D 1 7 2 0 2 3 2 2 2 5 2 8

Q14:

Consider the matrices 𝐴=−2107190, 𝐵=𝐴. Determine 𝑎 and 𝑏.

  • A 𝑎 = − 2 , 𝑏 = − 2
  • B 𝑎 = 1 0 , 𝑏 = 1 0
  • C 𝑎 = 9 , 𝑏 = 1
  • D 𝑎 = 1 0 , 𝑏 = − 2
  • E 𝑎 = − 2 , 𝑏 = 1 0

Q15:

Given that 𝐴=−26−6184, find 𝐴.

  • A 1 8 4 − 2 6 − 6
  • B − 6 4 6 8 − 2 1
  • C − 2 1 6 8 − 6 4
  • D 1 − 2 8 6 4 − 6

Q16:

Given that 𝐴=−59710−20637(𝐴+𝐵)=−13211243417−36,, determine the matrix 𝐵.

  • A − 8 1 1 6 − 5 5 1 1 0 − 3 − 1
  • B − 8 − 6 1 1 1 2 5 − 6 5 4 − 1
  • C − 8 − 5 1 0 1 1 5 − 3 6 1 − 1
  • D − 8 1 2 5 − 6 5 4 1 1 − 6 − 1

Q17:

Given that 𝐴=−7575−98𝐵=7−53−51−4,, find the result of 𝐴−𝐵, if possible.

  • A 1 4 − 1 0 − 2 4 − 6 − 1 2
  • BIt is not possible.
  • C − 1 4 2 6 1 0 − 4 1 2
  • D − 1 4 1 0 2 − 4 6 1 2
  • E 1 4 − 2 − 6 − 1 0 4 − 1 2

Q18:

Find 43+3[5−4].

  • A 1 2 2
  • B − 8 1 8
  • Cnot possible
  • D 1 9 − 9
  • E [ 1 9 1 5 ]

Q19:

Given that 𝑂 is a 3×3 zero matrix, find 𝑂.

  • A 1 0 0 0 1 0 0 0 1
  • B 0 1 1 1 0 1 1 1 0
  • C 1 1 1 1 1 1 1 1 1
  • D 𝐼
  • E 𝑂

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