To compute row reductions, feel free to use numerical applets such as this one from Georgia Tech, but make sure to state which row operations you have done, and to write the resulting matrix of each row operation.

Section 2.4: 2(b,d), 3(b,d), 4(b), 5(a,b), 7(b), 9(a,b,c), 20

Chapter 2 Review Exercises: 1(ii)(a,b) (Solve this using a row reduction applet), 6

Section 3.1: 1(b,d,f,h)

Review Exercise (not from the textbook): Let \( AX = B \) be a system of \( m \) equations in \( n \) variables, and assume there are more variables than equations (i.e. \( m\lt n \) ). Suppose the matrix \( A \) has rank \(m \). Does the system of equations always have a solution? Give a proof for your answer. (Hint: by row reduction, you may assume that the augmented matrix \( [A|B] \) is already in reduced row-echelon form. Use that this implies \( A \) is also in reduced row-echelon form. Given its rank, what form must \( A \) take?)