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Show that the elements on the main di...

Show that the elements on the main diagonal of a skew-symmetric matrix are all zero.

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To show that the elements on the main diagonal of a skew-symmetric matrix are all zero, we will follow these steps: ### Step 1: Definition of a Skew-Symmetric Matrix A matrix \( A \) is called skew-symmetric if it satisfies the condition: \[ A^T = -A \] where \( A^T \) is the transpose of matrix \( A \). ...
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Explore conceptually related problems

Which one of the following is wrong? 1.The elements on the main diagonal of a symmetric matrix are all zero 2. The elements on the main diagonal of a skew-symmetric matrix are all zero 3. For any square matrix A,(1)/(2)(A+A') is symmetric 4. For any square matrix A,(1)/(2)(A-A') is skew-symmetric

Which one of the following is wrong? (A) The elements on the main diagonal of a symmetric matrix are all zero (B) The elements on the main diagonal of a skew - symmetric matrix are all zero (C) For any square matrix A,AA' is symmetric (D) For any square matrix A,(A+A')^(2)=A^(2)+(A')+2AA'

Knowledge Check

  • The diagonal elements of a skew-symmetric matrix are:

    A
    unequal
    B
    zero
    C
    one
    D
    Insufficient data

  • The inverse of a skew symmetric matrix is

    A
    a symmetric matrix if it exists
    B
    a skew symmetric matrix if it exists
    C
    transpose of the original matrix
    D
    may not exist

  • Trace of a skew symmetric matrix is always equal to

    A
    `sum a_(ij)`
    B
    ` sum a_(ii)`
    C
    zero
    D
    none of these

    • Similar Questions

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    Prove that diagonal elements of a skew symmetric matrix are all zeroes.

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