Worksheet: Transpose of a Matrix

Download

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]
  • B44−5
  • C[5−4−4]
  • D[44−5]

Q2:

Given the matrix 𝐴=−84341−1, find 𝐴.

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

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=−422−7, 𝑋=44−1−7, does (𝑌−𝑋)=𝑌−𝑋?

  • ANo
  • BYes

Q5:

Find the transpose of the matrix −2−18.

  • A[−2−18]
  • B8−1−2
  • C[21−8]
  • D[8−1−2]

Q6:

Find the transpose of the matrix 0−81.

  • A[0−81]
  • B1−80
  • C[08−1]
  • D[1−80]

Q7:

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

  • A[7−3−2]
  • B−2−37
  • C[−732]
  • D[−2−37]

Q8:

Which of the following matrices is skew-symmetric?

  • A3−5−25−312−13
  • B0−3−530105−100
  • C0−1−910−6967
  • D10−9−2−9−2−5−2−54

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?

  • 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?

  • 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

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=−26−6184, find 𝐴.

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

Q16:

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

  • A−8116−55110−3−1
  • B−8−611125−654−1
  • C−8−510115−361−1
  • D−8125−65411−6−1

Q17:

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

Q18:

Find 43+3[5−4].

  • A122
  • B−818
  • Cnot possible
  • D19−9
  • 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=𝑖−𝑗
  • C𝑎=𝑖+𝑗
  • D𝑎=3𝑖+𝑗

Q22:

If 𝐴=1−123−34, then 3𝐴=.

  • A36−9−3912
  • B3−369−912
  • C69−9123−3
  • D−391236−9

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
  • D−1

Q25:

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

  • Askew-symmetric
  • Bdiagonal
  • Cunity
  • Dsymmetric

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.