Exercise 1: MATMUL

• You are asked to modify the program to handle arbitrarily sized matrices (up to some maximum). You might think therefore that the arrays should not be declared until the program has read in the appropriate sizes. However, this is not possible in C. Arrays must have their sizes fixed at compile time. You can get around this by sizing the arrays big enough to accommodate the maximum you really want to deal with. Then, at run time, when the "actual" sizes are read in, you can arrange for the program to use only as much or as little of the available array "space" as necessary - any left over can be simply ignored.

• The original program has four main parts: first the contents of array A are read in; then array B is read in; then the calculations are done (C is calculated); and, finally, C is printed out. The new program can reasonably retain this overall structure, so you should try to identify for yourself, exactly how the original program is broken down into these parts.

• In the reading of array A in the original program, a single scanf() call is used to read one entire row (four values). This is repeated three times to read the entire array. In the new program the width of the array is not fixed; so you cannot use a single scanf() call to read a whole row anymore. Instead you will have to use a single scanf() call to read just one value. This can then be embedded in a (new) for loop which iterates it for the correct number of columns so that one complete row is read. This whole loop can then be controlled by the "original" for loop, iterating over the rows (though with some further, minor, modification).

  Of course, similar considerations apply also to reading in the B array, and printing the C array.

• Note that multiple statements can be controlled, or iterated, by a single for statement. The set of statements to be iterated is simply enclosed in "curly brackets" or braces.

• The program MATMUL introduces a new operator, written +=. This is a combination of addition and assignment. The statement:

     x += y;

  is exactly equivalent to:

     x = (x + y);

  There are corresponding composite operators for all four basic arithmetic operations (addition, subtraction, multiplication, division). If you ever in doubt as to their effect, just write out the long form instead.