Describe the possible echelon forms for matrices with the fo

Describe the possible echelon forms for matrices with the following properties: A is a 2 times 2 matrix with linearly dependent columns. A is a 4 tomes 3 matrix, A = [a_1 a_2 a_3], such that {a_1, a_2} is linearly independent and a_3 is not in the span of a_1 and a_2.

Solution

describe the possibl echelon orms or matrices with the ollowing properties

A is 2*2 matrix with linearly dependnt columns

The linked entry contains the criteria for each, first the row echelon form, then additional criteria for reduced row echelon form. So using the term \"echelon form\", or even the casual use of the terms \"row echelon form\", can be ambiguous, depending on context, and depending on textbooks, to some degree, unless an explicit distinction is made.

Also, as an aside, consistency isn\'t a property of a matrix, per se, but of the system of equations that an augmented coefficient matrix may represent. For your matrices, the first reveals that there exist two linearly independent row (and column) vectors. Your second matrix reveals that the row vectors (and column vectors) are linearly dependent. We can also determine the rank of a matrix from a matrix in echelon form: the rank of a matrix is equal to the number of non-zero rows in the matrix when reduced to row echelon form.