What does it mean if a matrix has a row of zeros?

Matrices don’t have solutions. Matrices may represent systems of equations; systems of equations may have solutions. If all the entries in a row are zero, that row represents the equation 0=0, which can be ignored in deciding how many, if any, solutions a system has.

Can reduced echelon form have a row of zeros?

For a given matrix, despite the row echelon form not being unique, all row echelon forms and the reduced row echelon form have the same number of zero rows and the pivots are located in the same indices.

Does a row of zeros mean infinite solutions?

The answer is no whether or not the last row is zeros. The last row can be any linear combination of the first two rows leading to infinitely many solutions of the linear system, and the column vectors will always be linearly dependent.

When we put matrix A in reduced row echelon form we get the matrix This means that?

Definition We say that a matrix is in reduced row echelon form if and only if it is in row echelon form, all its pivots are equal to 1 and the pivots are the only non-zero entries of the basic columns. We show some matrices in reduced row echelon form in the following examples.

Does a row of zeros mean linearly dependent?

If we get a row of zeroes, then the vectors were linearly dependent, since we combined the rows above the zero row to get the row that became zero. Note also how spanning and independence are really opposite concepts.

Can a matrix with a row of zeros have an inverse?

Answer and Explanation: If a matrix A has a column or row of zeros, then detA=0 det A = 0 Consequently A does not admit inverse.

Does every matrix have a reduced row echelon form?

Understanding The Two Forms Any nonzero matrix may be row reduced into more than one matrix in echelon form, by using different sequences of row operations. However, no matter how one gets to it, the reduced row echelon form of every matrix is unique.

How do you tell if rows of a matrix are linearly independent?

Since the matrix is , we can simply take the determinant. If the determinant is not equal to zero, it’s linearly independent. Otherwise it’s linearly dependent. Since the determinant is zero, the matrix is linearly dependent.