Question

The third worksheet ("Ex. 3") contains 2 4x4 matrices, plus space for a third. Write a program that will read the first 2 matrices into array "B" and "C" . Create a 3rd array, "A" that is the result of matrix B + matrix C (i.e |A| = |B| + |C|). Output that array in the indicated cells (upper left = cell K1) To do this, use the rule for array addition for each matrix element: aij = bij + cij where i and j indicate the location (row, column) of the matrix element. NOTE: You must use arrays to get credit for this exercise. Keep close track of which loop is representing which index.

74	21	95	8		16	30	40	5
52	79	41	23	+	33	8	32	5	=
3	91	33	37		24	4	4	12
93	68	40	74		24	27	24	15

Answer 1

The program is basically keeping a track of addition of each element corresponding to the same indexes i,j and storing them in a third array of same size.

so, let us first understand the concept of array addition

Our program will basically add all the elements corresponding to i=1 i.e j=1,2,3,4 i.e 4 iterations. After the completion of i=1, it will move on to 2,3,4 respectively and add its iterations as well

As the language is not specified, for the comfort of students, I will be using basic C code.

*******************************************************************************************************************

#include <stdio.h>

#include <stdlib.h>

int main()

{

int i,j,k,s=0;

int a[4][4], b[4][4], c[4][4]; //declaring the three 4*4 arrays

//getting the input for array b

for(i=0;i<4;i++)

{for(j=0;j<4;j++)

{

scanf("%d",&b[i][j]);

}

}

//getting the input for array c

for(i=0;i<4;i++)

{for(j=0;j<4;j++)

{

scanf("%d",&c[i][j]);

}

}

//adding the corresponding elements of b and c and storing it in a

for(i=0;i<4;i++)

{for(j=0;j<4;j++)

{

a[i][j]=b[i][j]+c[i][j];

}

}

}

**************************************************************************************************************

An array always store values from 0,0 index, so our code will work upon 0,1,2,3 and its corresponding 4 iterations.

Now let us look for loop iterations.

loop 1 i=0:

i=0,j=0: 74+16

i=0,j=1: 21+30

i=0,j=2: 95+40

i=0,j=3: 8+5

loop 2 i=1:

i=1,j=0: 52+33

i=1,j=1: 79+8

i=1,j=2: 41+32

i=1,j=3: 23+5

loop 3 i=2:

i=2,j=0: 3+24

i=2,j=1:91+4

i=2,j=2:33+4

i=2,j=3:97+12

loop 4 i=3:

i=3,j=0: 93+24

i=3,j=1: 68+27

i=3,j=2: 40+24

i=3,j=3: 74+15

Therefore the final array A becomes

90	51	135	31
85	87	73	28
27	95	37	109
117	95	64	89