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Lesson Worksheet: Transpose of a Matrix Mathematics

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

Q1:

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

Q2:

Find the transpose of the matrix −544.

  • A[−544]
  • B44−5
  • C[5−4−4]
  • D[44−5]

Q3:

Which of the following matrices is symmetric?

  • A−2353−4−35−3−7
  • B−3−5−1−665−77−8
  • C−24−34−8−89−3−2
  • D−4−42−48−28−23

Q4:

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

  • A14−10−24−6−12
  • BIt is not possible.
  • C−142610−412
  • D−14102−4612
  • E14−2−6−104−12

Q5:

Given that 𝐴=−26−6184, find 𝐴.

  • A184−26−6
  • B−6468−21
  • C−2168−64
  • D1−2864−6

Q6:

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

Q7:

Given the matrix 𝐴=−84341−1, find 𝐴.

  • A−84341−1
  • B−84413−1
  • C−84341−1
  • D−84413−1

Q8:

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

  • ANo
  • BYes

Q9:

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

Q10:

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

This lesson includes 40 additional questions and 225 additional question variations for subscribers.

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