Lab $11$: Intro to $2$D Arrays

Exercise $1-$ Matrix Addition

$1.$ Write a function that adds two M x N matrices:

$($declare M and N as global constants where M $=2,$ N $=3)$

void matrixAdd$($ const int a$[][$N$],$ const int b$[][$N$],$ int sum$[][$N$])$;

The addition of two matrices is performed by adding elements in corresponding positions in the matrices. Therefore, matrices that are added must be of the same size; the result is another matrix of the same size.

Example of matrix addition:

$2.$ Input: The program should take in two matrices as input from the user in the following form: $($User input is underlined and bolded$)$

Enter Matrix A: $25103-1$

Enter Matrix B: $102-14-2$

$3.$ Output: The program should output the result of the sum of Matrix A and B in the following

form:

Res:

$353$

$-17-3$

Exercise $2-$ Matrix Multiplication

$1.$ Write a function that multiplies a Q x R matrix by a R x S matrix $($produces a Q x S matrix$)$:

$($declare Q$,$ R$,$ and S as global constants where Q $=2,$ R $=3,$ S $=3)$

void matrixMult$($const int a$[][$R$],$ const int b$[][$S$],$ int product$[][$S$])$;

Matrix multiplication is not computed by multiplying corresponding elements of the two matrices.

The value in position ci$,$j of the product C of two matrices A and B is the product of row i of the

first matrix and column j of the second matrix:

The product of row i and column j requires that the row i and the column j have the same

number of elements. Therefore, the first matrix $($A$)$ must have the same number of elements in

each row as there are in the columns of the second matrix $($B$).$ Thus, if A and B both have five

rows and five columns, their product has five rows and five columns. Furthermore, for these

matrices, we can compute both AB and BA$,$ but in general, they will not be equal.

$$ Another $($non$-$square$)$ example: if A has two rows and three columns and B has three

rows and three columns, the product AB will have two rows and three columns.

Given:

The first element in the product C $=$ AB is

$($Note: c$1,1$ will actually be stored in product$[0][0].)$

Similarly, we can compute the rest of the elements in the product of A and B:

$2.$ Input: The program should take in two matrices as input from the user in the following form:

Enter Matrix A$($size $2$x$3)$: $25103-1$

Enter Matrix B$($size $3$x$3)$: $102-14-2521$

Note: If cin breaks for any reason, all values in the array after that point must be $0.$ As long as you initialize your arrays to $0$ and then read directly into the array, it will work properly.

$3.$ Output: The program should output the result of the sum of Matrix A and B in the following

form:

Res:

$222-5$

$-810-7$

Note: Neither function should output anything. Any outputs should be in main.