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In linear algebra, a skew-symmetric matrix is a square matrix .....'A'
Rank of a matrix is used to find consistency of linear system of equations.As we know most of the engineering problems land up with the problem of finding solution of a linear system of equations ,at that point rank of matrix is useful.
When its matrix is non-singular.
by elimination,substitution or through the matrix method.
When its determinant is non-zero. or When it is a linear transform of the identity matrix. or When its rows are independent. or When its columns are independent. These are equivalent statements.
In linear algebra, a skew-symmetric matrix is a square matrix .....'A'
show that SQUARE MATRIX THE LINEAR DEPENDENCE OF THE ROW VECTOR?
Consider the linear system of equations AX = YwhereX is a n x 1 matrix of variables,Y is a n x 1 matrix of constants, andA is an n x n matrix of coefficients.Provided A is not a singular matrix, A has an inverse, A-1, an n x n matrix.Premultiplying by A-1 gives A-1AX = A-1Y or X = A-1Y, the solution to the linear system.
Rank of a matrix is used to find consistency of linear system of equations.As we know most of the engineering problems land up with the problem of finding solution of a linear system of equations ,at that point rank of matrix is useful.
When the matrix of coefficients is singular.
When its matrix is non-singular.
the invarient point is the points of the graph that is unaltered by the transformation. If point (5,0) stays as (5,0) after a transformation than it is a invariant point The above just defines an invariant point... Here's a method for finding them: If the transformation M is represented by a square matrix with n rows and n columns, write the equation; Mx=x Where M is your transformation, and x is a matrix of order nx1 (n rows, 1 column) that consists of unknowns (could be a, b, c, d,.. ). Then just multiply out and you'll get n simultaneous equations, whichever values of a, b, c, d,... satisfy these are the invariant points of the transformation
by elimination,substitution or through the matrix method.
If it is not a square matrix. You cannot invert a square matrix if it is singular. That means that at least one of the rows of the matrix can be expressed as a linear combination of the other rows. A simple test is that a matrix cannot be inverted if its determinant is zero.
A = coefficient matrix (n x n) B = constant matrix (n x 1)
When its determinant is non-zero. or When it is a linear transform of the identity matrix. or When its rows are independent. or When its columns are independent. These are equivalent statements.
Evar D. Nering has written: 'Linear algebra and matrix theory' -- subject(s): Linear Algebras 'Linear programs and related problems' -- subject(s): Linear programming