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

Q2:

Given the matrix 𝐴=843411, 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=4227, 𝑋=4417, does (𝑌𝑋)=𝑌𝑋?

  • ANo
  • BYes

Q5:

Find the transpose of the matrix 218.

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

Q6:

Find the transpose of the matrix 081.

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

Q7:

Find the transpose of the matrix 732.

  • 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=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?

  • 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=266184, 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=5971020637(𝐴+𝐵)=1321124341736,, 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=757598𝐵=753514,, find the result of 𝐴𝐵, 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[54].

  • 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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