HOW TO FIND THE RANK OF A MATRIX?

Is there any easy way to find the rank of a 4*4 matrix? Can we find rank of a non square matrix?

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6 Answers
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  • The rank of a matrix is defined as (a) the maximum number of linearly independent column vectors in the matrix or (b) the maximum number of linearly independent row vectors in the matrix. Both definitions are equivalent.
    For an r x c matrix,
    If r is less than c, then the maximum rank of the matrix is r.
    If r is greater than c, then the maximum rank of the matrix is c.
    The rank of a matrix would be zero only if the matrix had no elements. If a matrix had even one element, its minimum rank would be one.
    How to Find Matrix Rank
    In this section, we describe a method for finding the rank of any matrix. This method assumes familiarity withechelon matrices and echelon transformations.
    The maximum number of linearly independent vectors in a matrix is equal to the number of non-zero rows in its row echelon matrix. Therefore, to find the rank of a matrix, we simply transform the matrix to its row echelon form and count the number of non-zero rows.
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  • The rank of a matrix is defined as (a) the maximum number of linearly independent column vectors in the matrix or (b) the maximum number of linearly independent row vectors in the matrix. Both definitions are equivalent.
    For an r x c matrix,
    If r is less than c, then the maximum rank of the matrix is r.
    If r is greater than c, then the maximum rank of the matrix is c.
    The rank of a matrix would be zero only if the matrix had no elements. If a matrix had even one element, its minimum rank would be one.
    How to Find Matrix Rank
    In this section, we describe a method for finding the rank of any matrix. This method assumes familiarity withechelon matrices and echelon transformations.
    The maximum number of linearly independent vectors in a matrix is equal to the number of non-zero rows in itsrow echelon matrix. Therefore, to find the rank of a matrix, we simply transform the matrix to its row echelon form and count the number of non-zero rows.
    0
  • use echleon transformation to solve 4*4 matrix
    we can not find rank of non square matrix
    0
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