# Thread: urgent.-reduced row echelon form R,.....S

1. ## urgent.-reduced row echelon form R,.....S

Hi does anyone know how to do this question? im unsure about the theory as well.thanks.
If A is a 7x5 matrix with reduced row echelon form R and B is a 4x6 matrix with reduced row echelon form S. Which of the following statements are always true.

R has at least one zero row/ S has at least one zero row/R has at least one column without a leading one /S has at least one column without a leading one /The system Ax=b has at least one solution for all b which is an element of R7/The system Bx=0 has infinitely many solutions .

2. ## Re: urgent.-reduced row echelon form R,.....S

A 7x5 matrix has 7 rows, five columns. Row Reduction constructs a stairstep pattern. If the columns are linearly independent, the RREF will show a diagonal of ones with zeroes above and below. Note that this is the "most common case," in the sense that if you generate a random matrix it's very unlikely this is what you'll get.

I can't seem to get the latex to work right now, but R will "almost certainly" have a 1 in the top left, and a diagonal of 1's, everything else 0. There will be two rows of zeroes at the bottom.