Start Maple 2021 from the desktop, Start Menu/All apps/M, or otherwise. Maple has two modes, Worksheet and Document. You can use either, but Worksheet is more like a calculator rather than a word processor and is easier to use. To start one or the other use File/New Every Maple command should end with a semi-colon ";" for instance > 2+5; The answer will appear in the middle of the line following. If you forget the semi colon Maple wont actually complain, usually, though. Every time I give you a command to use in this sheet I will give the > symbol in front. You are free to copy the command from this file and paste into Maple, this will ensure you don't make a mistake when typing the command in. Don't include the ">"! Multiplication of numbers uses *, division uses / and powers are ^. Notice that Maple does not use decimals by default, and neither will I, as we can lose accuracy that way. We can use ":=" to assign a value to a name, usually a letter > a := -22; We can also set, for example, > c := 7; A common mistake is to forget the : in := since Maple will still show "c=7" but c will not be assigned the value 7 in Maple's memory. #Q1: [1 mark] Pick several integers and combine them using these two symbols and brackets and make sure you get the answers you expect when you press enter. ( You can write any comments in the worksheet by starting a line with # ) Verify that c-a is not 0 and a/c gives a fraction, but 3.0/c doesn't For an unknown variable, such as b, Maple will just report that name: > a+b; Now set b to be some randomly chosen integer and note that the line above doesn't change but when you again ask for > a+b; it should give a number now instead. Maple works sequentially so I STRONGLY encourage you to work down the worksheet without editing earlier lines so that the confusion is lessened. ( If you need to you can go back up the worksheet and insert new lines if necessary using control-j or control-k. You can reset a variable's v's value to unknown using > v:='v'; ) In the other labs I will use capital letters for matrices, usually with a number after them, and lower case letters for numbers, but it isn't mandatory. When I introduce a Maple function it is a good idea to read the help page for that function. You can do that for the function sqrt by visiting http://www.maplesoft.com/support/help/Maple/view.aspx?path=sqrt and can search for any other function in that webpage too. You can also do it by using the Maple "Help" menu or by typing > ?sqrt However, ? can be slow to work, and might crash your computer. To recover, press the octagonal red octagon button marked "stop". To exit from the help page, close the subwindow, use alt-tab or the Window menu to move between them. #Q2: [1 mark] Use sqrt to see how Maple shows the square roots of c, 10 and 10.0. Write a comment to explain what you see. Remember that you should save your worksheet on your computer regularly, and even use different names each time, as we will also do for the matrices, just in case you lose power or something corrupts your worksheet. If you have to reload your worksheet Maple will show what you did, but not have the answers in memory, so you will have to rerun your commands. This is another reason why it is good to not erase anything and work sequentially. We are now ready to do some matrix algebra... Load all of the linear algebra progams with the command: > with(LinearAlgebra); All the new commands listed are now known by Maple, we will use some. We can create a 3x4 augmented matrix by using the following command > B0:=Matrix(3, 4, [[2, 1, 5, 3], [4, 1, 1, 1], [3, 1, 2, 0]]); This form gives the matrix in terms of its rows. Even though we are using this to represent a system of equations Maple doesn't give a dotted line, but we should try to remember it is there. Notice that we again use ":=" to assign a value to B0. I recommend using a capital letter for all matrices, but Maple will not insist on that. Note that all of the LinearAlgebra commands also begin with a capital letter, although "matrix" is also defined, it will not always work properly. We can do the three different row operations as follows: > B1:=RowOperation(B0,[2,1],7); will add 7 copies of row 1 of B0 to row 2 and create a matrix B1 > B2:=RowOperation(B1,[3,2]); will switch row 3 and row 2 in B1 and make a matrix B2 > B3:=RowOperation(B2,3,1/2); will multiply row 3 by 1/2 and form a matrix B3 ( In general N:=RowOperation(M,[p,q],r) takes matrix M and turns it into matrix N using "Row p <-- Row p + r times Row q" and the other two operations are similar. Note that when we switch rows we use ,[p,q] and when we multiply a row we use ,p,r ) I recommend using the scheme of naming each matrix sequentially, and try to not reuse any name, if you don't get the matrix you wanted, just use the next Bnumber matrix with a previous one. Note that the given B3 still has no zeros on the left of the dotted line, so the Row Operations I chose didn't help. The zero to the right of the dotted line isn't relevant. Q3: [4 marks] Find a sequence of row operations that eventually produce 6 zeros and 3 ones on the left of the dotted line from B3. I recommend first making two zeros in the 2nd column as it has the smallest numbers. Check your answers for x, y and z give you the correct answers to the original equations. You can set x:= , y:= and z:= your values then evaluate: > 2*x + y + 5*z; > 4*x + y + z; > 3*x + y + 2*z; and check that these are the same numbers on the right of B0's dotted line. Q4: [4 marks] Maple can create random matrices to practise with: > randomize(Value(Time())): E0:=RandomMatrix(3,4,generator=rand(3..11)); Use Row Operations starting with E0 to get as many zeros as possible. Note that the numbers in this matrix are between 3 and 11, so you should probably consider making a 1 as your first row operation. Remember you will be doing this on paper a week from today! You can check what Maple thinks the final solution should be using: > ReducedRowEchelonForm(E0); Do you believe your answer is essentially the same as Maple's? Once you have completed all of these activities, please save your worksheet then use File / Export As and choose pdf. Now upload the file to Crowdmark.