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Worksheet: Symmetric and Skew-Symmetric Matrices

Q1:

If is a symmetric matrix, what are the values of , , and ?

  • A , ,
  • B , ,
  • C , ,
  • D , ,
  • E , ,

Q2:

If is a symmetric matrix, what are the values of , , and ?

  • A , ,
  • B , ,
  • C , ,
  • D , ,
  • E , ,

Q3:

Which of the following matrices is skew-symmetric?

  • A
  • B
  • C
  • D

Q4:

Which of the following matrices is skew-symmetric?

  • A
  • B
  • C
  • D

Q5:

Which of the following matrices is skew-symmetric?

  • A
  • B
  • C
  • D

Q6:

If 𝐴 and 𝐡 are symmetric matrices, does it follow that 𝐴 𝐡 is also symmetric?

  • Ano
  • Byes

Q7:

Given that the following matrix is skew-symmetric, find the value of π‘₯ + 𝑦 + 𝑧 .

Q8:

Given that the following matrix is skew-symmetric, find the value of π‘₯ + 𝑦 + 𝑧 .

Q9:

Given that the following matrix is skew-symmetric, find the value of π‘₯ + 𝑦 + 𝑧 .

Q10:

Suppose that 𝐴 and 𝐡 are symmetric matrices and that 𝐴 𝐡 = 𝐡 𝐴 . Does it follow that 𝐴 𝐡 is also a symmetric matrix?

  • Ayes
  • Bno

Q11:

Find the value of which makes the following a symmetric matrix.

Q12:

Find the value of which makes the following a symmetric matrix.

Q13:

Find the value of which makes the following a symmetric matrix.

Q14:

The non-zero eigenvalues of a real, skew-symmetric matrix are .

  • Apurely real
  • Bnon-negative
  • Cpurely imaginary

Q15:

Which of the following matrices is symmetric?

  • A
  • B
  • C
  • D

Q16:

Which of the following matrices is symmetric?

  • A
  • B
  • C
  • D