I am very new to linear algebra and am having a bit of trouble understanding exactly what reduced row echelon form and row echelon form mean. From what I know, if a matrix is reduced row echelon form, it is always also row echelon form?
a) It follows the rule that "any row that consists of only zeroes is at the bottom of the matix", so so far it follows the definition for reduced row echelon form.
The first non-zero entry in each other row is 1: It follows this too, so so far so good.
The leading 1 of each row, after the first row, lies to the right of the leading 1 of the previous row: This is where I get confused. The whole second column is filled with zeroes, but I thought it should always be completely diagonal along the matrix (the leading 1s that is)?
What really confuses me is I thought there is supposed to be a leading 1 on every row? If the bottom row is all zeroes that is not the case. Is the bottom an exception or something, it can be all zeroes and not have a leading 1?
For a matix to be reduced row echelon form, is it correct to say that all numbers above and below the leading 1 in a column have to be 0?
What also really confuses me is the last column, isn't this the constant column? Do the same rules apply to this column?
For d), it looks like the leading 1 doesn't start until row 2. Or it is in the constant column, which makes it out of the diagonal line.