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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.
How do you generate generator matrix in linear block code when a code word is given?
The generator matrix is made out of that code word and all the possibilities for the code words. The number of rows of the generator matrix are the number of message bits and the number of columns are equal to the total number of bits i.e parity bits + message bits. The only necessary condition is that each row of generator matrix is linearly independent of the other row.
A system of two linear equations has infinitely many solutions if?
One equation is simply a multiple of the other. Equivalently, the equations are linearly dependent; or the matrix of coefficients is singular.
Is it possible to multiply a 3 X 2 matrix and a 2 X 3 matrix?
The first matrix has 3 rows and 2 columns, the second matrix has 2 rows and 3 columns. Two matrices can only be multiplied together if the number of columns in the first matrix is equal to the number of rows in the second matrix. In the example shown there are 3 rows in the first matrix and 3 columns in the second matrix. And also 2 columns in the first and 2 rows in the second. Multiplication of the two matrices is therefore possible.
A rectangular arrangement of numbers in rows and columns?
It is a matrix or a determinant.
What does it signify when an eigenvalue of a matrix is equal to 0?
When an eigenvalue of a matrix is equal to 0, it signifies that the matrix is singular, meaning it does not have a full set of linearly independent eigenvectors.
How can you tell if a matrix is invertible?
An easy exclusion criterion is a matrix that is not nxn. Only a square matrices are invertible (have an inverse). For the matrix to be invertible, the vectors (as columns) must be linearly independent. In other words, you have to check that for an nxn matrix given by {v1 v2 v3 ••• vn} with n vectors with n components, there are not constants (a, b, c, etc) not all zero such that av1 + bv2 + cv3 + ••• + kvn = 0 (meaning only the trivial solution of a=b=c=k=0 works).So all you're doing is making sure that the vectors of your matrix are linearly independent. The matrix is invertible if and only if the vectors are linearly independent. Making sure the only solution is the trivial case can be quite involved, and you don't want to do this for large matrices. Therefore, an alternative method is to just make sure the determinant is not 0. Remember that the vectors of a matrix "A" are linearly independent if and only if detA�0, and by the same token, a matrix "A" is invertible if and only if detA�0.
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.
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.
How do you generate generator matrix in linear block code when a code word is given?
The generator matrix is made out of that code word and all the possibilities for the code words. The number of rows of the generator matrix are the number of message bits and the number of columns are equal to the total number of bits i.e parity bits + message bits. The only necessary condition is that each row of generator matrix is linearly independent of the other row.
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.
A system of two linear equations has infinitely many solutions if?
One equation is simply a multiple of the other. Equivalently, the equations are linearly dependent; or the matrix of coefficients is singular.
What is a matrix with the same number of rows as columns?
A matrix having the same number of rows and columns is a SQUARE MATRIX.
What is the matrix's in oder?
Restate the question: "What is the order of a matrix?" The order of a matrix tells the number of rows and columns in the matrix. For instance, a matrix with 3 rows and 4 columns is a 3x4 matrix ("three by four"). A square matrix has the same number of rows and columns: 2x2
Is it possible to multiply a 3 X 2 matrix and a 2 X 3 matrix?
The first matrix has 3 rows and 2 columns, the second matrix has 2 rows and 3 columns. Two matrices can only be multiplied together if the number of columns in the first matrix is equal to the number of rows in the second matrix. In the example shown there are 3 rows in the first matrix and 3 columns in the second matrix. And also 2 columns in the first and 2 rows in the second. Multiplication of the two matrices is therefore possible.
How can you find the demensions of a matrix?
You count the rows and columns. "Dimensions" simply means how many rows and how many columns the matrix has.
How do you find transportation of matrix?
Invert rows and columns to get the transpose of a matrix
