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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.
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How do you find rank of a matrix?
First, You have to reduce the matrix to echelon form . The number of nonzero rows in the reduced echelon form matrix (number of linearly independent rows) indicates the rank of the matrix. Go to any search engine and type "Rank of a matrix, Cliffnotes" for an example.
If rank of the matrix is equal to no of variable then it have?
Then it has (not have!) a unique solution.
What is the difference between tensors and matrices?
A scalar, which is a tensor of rank 0, is just a number, e.g. 6 A vector, which is a tensor of rank 1, is a group of scalars, e.g. [1, 6, 3] A matrix, which is a tensor of rank 2, is a group of vectors, e.g. 1 6 3 9 4 2 0 1 3 A tensor of rank 3 would be a group of matrix and would look like a 3d matrix. A tensor is the general term for all of these, and the generalization into high dimensions.
Are the image and kernel of a 3x3 matrix ever equal If so give an example?
No.A 3x3 matrix A is a representation of a linear map \alpha : \mathbb{R}^3 \longrightarrow \mathbb{R}^3 .For any linear map T : U \longrightarrow V ,we have the rank-nullity theorum:rank(T)+nullity(T) = dim(U)where the rank and nullity are the dimensions of the image and kernal of T respectively.Im(T) = ker(T) \Rightarrow rank(T) = nullity(T) = m, sayfor some non-negative integer m. Then the rank-nullity theorum implies that dim(U)=2m.The image and kernal of a matrix A are the same as those for the corresponding basis-free linear map \alpha .For a 3x3 matrix, dim(U) = 3, so there are no such matrices (since 3 is odd).
How do i solve rank of a determinant?
Matrix inverses and determinants, square and nonsingular, the equations AX = I and XA = I have the same solution, X. This solution is called the inverse of A.
How do you find rank of a matrix?
First, You have to reduce the matrix to echelon form . The number of nonzero rows in the reduced echelon form matrix (number of linearly independent rows) indicates the rank of the matrix. Go to any search engine and type "Rank of a matrix, Cliffnotes" for an example.
Does the squaring of matrix change its rank?
No, it does not.
The rank of product of two matrices cannot exceed the rank of either factor?
The statement that the rank of product of two matrices cannot exceed the rank of either factor is a true statement. The rank of a matrix is the largest number of linearly independent rows or columns. The column rank is equal to the row rank in every matrix.
If rank of the matrix is equal to no of variable then it have?
Then it has (not have!) a unique solution.
What is the application of sparse matrix?
A sparse matrix is matrix that allows special techniques to take advantage of large number of zero element. Application of sparse matrix is classification and relationship analysis in large data base system - SPARCOM
What measures application for concepts?
content-performance matrix, what measures application for concepts?
Why do square matrices only have multiplicative inverses?
there are pseudo inverses for non-square matrices a square matrix has an inverse only if the original matrix has full rank which implies that no vector is annihilated by the matrix as a multiplicative operator
Examples of nullity of a matrix?
A null matrix is a matrix with all its elements zero.EXAMPLES : (0 0) is a null row matrix.(0 0)(0 0) is a null square matrix.NOTE : Text handling limitations prevent the printing of large brackets to enclose the matrix array. Two pairs of smaller brackets have therefore been used.Answer 2:The above answer is a null matrix. However, the nullity of a matrix is the dimension of the kernel. Rank + Nullity = Dimension. So if you have a 4x4 matrix with rank of 2, the nullity must be 2. This nullity is the number of "free variables" you have. A 4x4 matrix is 4 simultaneous equations. If it is rank 2, you have only two independent equations and the other two are dependent. To solve a system of equations, you must have n independent equations for n variables. So the nullity tells you how short you are in terms of equations.
What is the difference between tensors and matrices?
A scalar, which is a tensor of rank 0, is just a number, e.g. 6 A vector, which is a tensor of rank 1, is a group of scalars, e.g. [1, 6, 3] A matrix, which is a tensor of rank 2, is a group of vectors, e.g. 1 6 3 9 4 2 0 1 3 A tensor of rank 3 would be a group of matrix and would look like a 3d matrix. A tensor is the general term for all of these, and the generalization into high dimensions.
Does the ring of full rank square matrices form a domain?
It would form a domain, except that it fails to even be a ring. The 0 matrix has rank 0, so it is never a full rank matrix - therefore the set of full rank square matrices doesn't have an additive identity. It is true that there are no zero divisors among the full rank square matrices: if AB=0, and A has full rank, then it's invertible, so A-1AB=A-10, or B=0. Similarly, if BA=0, BAA-1=0A-1 so B=0.
What is the rank of 44 matrix whoose first 2 rows are linearly independent and any 3 columns are dependent?
2
What is the determinant rank of the determinant of 123456 its a 2 x 3 matrix?
A determinant is defined only for square matrices, so a 2x3 matrix does not have a determinant.Determinants are defined only for square matrices, so a 2x3 matrix does not have a determinant.
