5. Matrix Operations Suppose now you put in a matrix and you wish to manually do row operations to it. MATLAB doesn't have any functions for doing row operations, instead we have to execute low-level commands to do so. We will use "array slicing." This is easier than it seems. Here is an augmented matrix >> A=[1-1 -37; -3 1 4 -16; 4-3 -5 12] To get this to row echelon form, first we'll clean out the entries below the upper-left 1. To do this we need to add 3 times row 1 to row 2. In MATLAB the code is >> A(2,:)=A(2,:)+3*A(1,:) Confused? I was! The expression A(rownumber, :) refers to the entire row, so basically this line is saying: A(2,:)=A(2,:)+3+A(1,:) Row 2 Row 2 3+Row1 Try it! The result will be given. Next we'll add -4 times row 1 to row 3. >> A(3,:)=A(3,:)+(-4)+A(1,:) Now you'll see that we have Os below the upper-left 1. Next we need to get a 0 in the bottom row where the 1 is. The easiest way to do this is first to interchange rows 2 and 3. >> A([23], :)=A([32], :) This is a confusing command but it does the job. Now we add twice row 2 to row 3. >> A(3,:) A (3,:)+2+A(2,:) The result you'll see is the matrix in row echelon form. Remember this means any rows of Os are at the bottom (none in this case) and the leading entries go down and right. To get to reduced row echelon form, we first have to get 1s for all our leading entries. The third row 2. Consider the system of equations 12x2 3x3 + 2x4 − - - x5=-7 -2x19x26x38x4+16x5 = 14 - -17x2+3x3 2x4 +115=-3 4x18x212x3 + 4x5=-8 (a) Enter it into MATLAB as an (augmented) matrix named B. (b) Use elementary row operations (as in part 5 of the guide) to reduce it to row echelon form. (c) Continue using elementary row operations to get to reduced row echelon form. Yes, you have to. (d) Re-enter the original matrix into MATLAB and use the rref command to instantly get the reduced row echelon form. Make sure it is the same as your previous answer. (From this point onward, we will make extensive use of the rref command in MATLAB. You do not need to do row reduction in MATLAB one elementary row operation at a time anymore.) (e) Give the solution of the system in parametric vector form. 3. Start this problem in format short. Consider the linear system whose augmented matrix is 2 2 -7 A = 3 1 -1 0 -6 6 -5 (a) Use the rref command to give the reduced row echelon form of A. Make sure your result in presented in decimals, not fractions. (b) Write the solution of the linear system which corresponds to A in decimals, not fractions. (Your "solution" is actually a decimal approximation to the solution.) (c) Give the reduced row echelon form of A in fractions rather than decimals. (d) Write the solution of the linear system which corresponds to A in fractions, not decimals.