Respuesta :
False , If matrix A is in reduced row-echelon form, then at least one of the entries in each column must be 1.
Sure, yours is a good counterexample. One could give an example that involves less typing, like the 1×1 zero matrix! Maybe pedagogically better is the 2×2, first row 10, second row 00.
What is the reduced row echelon form for the matrix?
- If the leading coefficient in each row is the only non-zero number in that column, the matrix is said to be in reduced row echelon form.
- A 3x5 matrix in reduced row echelon form. Row echelon forms are commonly encountered in linear algebra, when you'll sometimes be asked to convert a matrix into this form.
Can reduced row echelon form have a column of zeros?
- In a logical sense, yes. The zero matrix is vacuously in RREF as it satisfies: All zero rows are at the bottom of the matrix.
- The leading entry of each nonzero row subsequently to the first is right of the leading entry of the preceding row.
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