Hello, i have a problem that asks me to put in reduced row echelon form and I have no clue how to even begin.
Let A be a 4X5 matrix. If a1,a2,a4 are linearly independent and
a3=a1-3a2
a5=a1-2a2-3a4
determine the reduced row echelon form of A.
Any help is greatly appreeciated.
Thank You,
Diggidy
try this: do you know of any "ready-to-eat" basis sets for R^4? let's say you did: B = {b1,b2,b3,b4}.
try setting the 1st column of A to b1, the 2nd column of A to b2, and the 4th column of A to b3, and the other two columns as per instructed.
you know that the basis elements are linearly independent. plug in the numbers and see what the matrix looks like. is it row-reduced?
if a1 = (1,0,0,0) and a2 = (0,1,0,0) then a1 - 2a2 = (1,0,0,0) - 2(0,1,0,0) = (1,0,0,0) + (0,-2,0,0) = (1,-2,0,0)
that is NOT what i see as your third column. column vectors add and subtract just as other vectors do: coordinate-by-coordinate.
if a4 = (0,0,1,0), then a1-2a2-3a4 = (1,0,0,0) - 2(0,1,0,0) - 3(0,0,1,0) = (1,0,0,0) + (0,-2,0,0) + (0,0,-3,0) = (1,-2,-3,0).
again, this is not what i see as your 4th column.
and why the =0 at the end? the matrix is NOT equal to 0.