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What is the symbol for skew?
In linear algebra, a skew-symmetric matrix is a square matrix .....'A'
When will the system of linear equation be consistent?
When its matrix is non-singular.
What is the application for rank of the matrix?
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.
How can you solve a linear equation?
by elimination,substitution or through the matrix method.
When is a square matrix said to be diagonisable?
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.
What is the significance of the eigensystem in the context of linear algebra and how is it used to analyze matrices?
The eigensystem in linear algebra is important because it helps us understand how a matrix behaves when multiplied by a vector. It consists of eigenvalues and eigenvectors, which provide information about the matrix's properties. By analyzing the eigensystem, we can determine important characteristics of the matrix, such as its stability, diagonalizability, and behavior under repeated multiplication.
What is the symbol for skew?
In linear algebra, a skew-symmetric matrix is a square matrix .....'A'
Show that for a square matrix the linear dependence of the row vectors implies that of the column vectors and conversely.?
show that SQUARE MATRIX THE LINEAR DEPENDENCE OF THE ROW VECTOR?
What are the matrix method of linear systems?
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.
When will the system of linear equation be consistent?
When its matrix is non-singular.
When will a system of linear equations be inconsistent?
When the matrix of coefficients is singular.
What is the application for rank of the matrix?
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.
How do you determine the invariant point in a transformation of a relation?
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
How can you solve a linear equation?
by elimination,substitution or through the matrix method.
When can you not invert a matrix?
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.
What is the significance of the sigma matrix in the context of linear algebra and how is it used in mathematical computations?
The sigma matrix, also known as the covariance matrix, is important in linear algebra because it represents the relationships between variables in a dataset. It is used to calculate the variance and covariance of the variables, which helps in understanding the spread and correlation of the data. In mathematical computations, the sigma matrix is used in various operations such as calculating eigenvalues and eigenvectors, performing transformations, and solving systems of linear equations.
What does the backslash operator do in MATLAB and how is it used in matrix operations?
In MATLAB, the backslash operator () is used for solving systems of linear equations. It performs matrix left division, which is equivalent to solving the equation Ax B for x, where A is the coefficient matrix and B is the right-hand side matrix. The backslash operator is commonly used to find the solution to a system of linear equations in MATLAB.
