For Ax b let the reduced echelon form of Ab be 100T 010T 3

For Ax = b, let the reduced echelon form of [A|b] be:

[(1,0,0)^T, (0,1,0)^T, (3, -2, 0)^T, (0,0,1)^T, (5,3,1)^T]

a. Does the equation Ax=c have a solution for each c in R³? Explain.

b. Find bases for the Null(A) and Row(A) and find their dimensions.

c. Find the projection of (5,3,1,0)^T onto Null(A) and its distance to Null(A).

Thank you for any and all help in advance!

Solution