Worksheet: Transpose of a Matrix

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[544]
  • B445
  • C[544]
  • D[445]

Q2:

Given the matrix 𝐴=843411, find 𝐴.

  • A843411
  • B844131
  • C843411
  • D844131

Q3:

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

  • A4×4
  • B4×1
  • C1×1
  • D1×4

Q4:

Given the matrices 𝑌=4227, 𝑋=4417, does (𝑌𝑋)=𝑌𝑋?

  • ANo
  • BYes

Q5:

Find the transpose of the matrix 218.

  • A[218]
  • B812
  • C[218]
  • D[812]

Q6:

Find the transpose of the matrix 081.

  • A[081]
  • B180
  • C[081]
  • D[180]

Q7:

Find the transpose of the matrix 732.

  • A[732]
  • B237
  • C[732]
  • D[237]

Q8:

Which of the following matrices is skew-symmetric?

  • A352531213
  • B03530105100
  • C019106967
  • D1092925254

Q9:

Given that the matrix 𝐵=02𝑥63𝑧+1403𝑧3𝑦+6𝑥120 is skew-symmetric, find the value of 𝑥+𝑦+𝑧.

Q10:

Find the value of 𝑥 which makes the matrix 𝐴=15𝑥3438 symmetric.

Q11:

If 𝐴=62𝑦𝑦3𝑥𝑧+59𝑧692𝑥114 is a symmetric matrix, what are the values of 𝑥, 𝑦, and 𝑧?

  • A𝑥=9, 𝑦=12, 𝑧=17
  • B𝑥=9, 𝑦=0, 𝑧=17
  • C𝑥=6, 𝑦=0, 𝑧=5
  • D𝑥=9, 𝑦=0, 𝑧=5
  • E𝑥=9, 𝑦=0, 𝑧=5

Q12:

Which of the following matrices is symmetric?

  • A235343537
  • B351665778
  • C243488932
  • D442482823

Q13:

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

  • A232017282523
  • B222528172023
  • C172220252328
  • D172023222528

Q14:

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

  • A𝑎=2, 𝑏=2
  • B𝑎=10, 𝑏=10
  • C𝑎=9, 𝑏=1
  • D𝑎=10, 𝑏=2
  • E𝑎=2, 𝑏=10

Q15:

Given that 𝐴=266184, find 𝐴.

  • A184266
  • B646821
  • C216864
  • D128646

Q16:

Given that 𝐴=5971020637(𝐴+𝐵)=1321124341736,, determine the matrix 𝐵.

  • A81165511031
  • B86111256541
  • C85101153611
  • D81256541161

Q17:

Given that 𝐴=757598𝐵=753514,, find the result of 𝐴𝐵, if possible.

  • A141024612
  • BIt is not possible.
  • C142610412
  • D141024612
  • E142610412

Q18:

Find 43+3[54].

  • A122
  • B818
  • Cnot possible
  • D199
  • E[1915]

Q19:

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

  • A100010001
  • B011101110
  • C111111111
  • D𝐼
  • E𝑂

Q20:

If 𝐴=𝑎𝑏𝑐𝑑 is a skew-symmetric matrix, then 7𝑏+5𝑐=.

  • A7𝑎+5𝑑
  • B2𝑏+𝑑
  • C5𝑎+7𝑑
  • D5𝑏+7𝑐

Q21:

If 𝐴 is a symmetric matrix, then which of the following can be a rule to deduce the element of matrix 𝐴?

  • A𝑎=3𝑖+2𝑗
  • B𝑎=𝑖𝑗
  • C𝑎=𝑖+𝑗
  • D𝑎=3𝑖+𝑗

Q22:

If 𝐴=112334, then 3𝐴=.

  • A3693912
  • B3369912
  • C6991233
  • D3912369

Q23:

If 𝐴 and 𝐵 are two symmetric matrices, then matrix 𝐴𝐵𝐴 is .

  • Asymmetric
  • Btriangular
  • Cskew symmetric
  • Ddiagonal

Q24:

If 𝑎𝑏𝑐𝑥𝑦𝑧𝑢𝑣𝑤 is skew symmetric, then 𝑎+𝑏+𝑐+𝑧𝑢+𝑣+𝑤+𝑥=.

  • A1
  • B𝑎𝑤
  • C0
  • D1

Q25:

If 𝐴 is a square matrix and 𝐴+𝐴=𝑂, then 𝐴 is a matrix.

  • Askew-symmetric
  • Bdiagonal
  • Cunity
  • Dsymmetric

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