Solving Zero Matrix

Introduction :

The zero matrix is defined as the one which consists of the number zero in all the entries. For example consider 2 x 2 matrix which have 4 elements (2 in each row or column). For zero matrix, the four elements are having zero values. consider 2 x 3 matrix which have 6 elements (3 in each row). For this zero matrix, the six elements are having zero values.

Examples to Explain "solving Zero Matrix "

A matrix O = [oij]m × n is defined to be a zero matrix or said to be null matrix having all the entries zero which is denoted by O    

`O_1` = [ 0 ] ;  `O_2` = `[[0,0],[0,0]]`    `O_3` =   `[[0,0,0],[0,0,0],[0,0,0]] `   `O_4` =  `[[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0]] `    `O_5` =  `[[0,0,0,0,0],[0,0,0,0,0],[0,0,0,0,0],[0,0,0,0,0],[0,0,0,0,0]] `    and so on   

Multiply this matrix  `[[93,91,91],[92,92,90],[91,92,91]]` with the zero matrix  `[[0,0,0],[0,0,0],[0,0,0]]`   
Solution:

It is given by    `[[93.0+91.0+91.0,93.0+91.0+91.0,93.0+91.0+91.0],[92.0+92.0+90.0,92.0+92.0+90.0,92.0+92.0+90.0],[91.0+92.0+91.0,91.0+92.0+91.0,91.0+92.0+91.0]]`      

`= [[93.0+91.0+91.0,93.0+91.0+91.0,93.0+91.0+91.0],[92.0+92.0+90.0,92.0+92.0+90.0,92.0+92.0+90.0],[91.0+92.0+91.0,91.0+92.0+91.0,91.0+92.0+91.0]]`     

` = [[0+0+0,0+0+0,0+0+0],[0+0+0,0+0+0,0+0+0],[0+0+0,0+0+0,0+0+0]]`        

= `[[0,0,0],[0,0,0],[0,0,0]]`     is the zero matrix obtained here.

Perform the subtraction operation on the matrix  `[[33,32,31],[32,32,30],[31,32,31]]` and     `[[33,32,31],[32,32,30],[31,32,31]]` 
Solution:

These matrix are with same rows (3) and columns (3)

= `[[33-33,32-32,31-31],[32-32,32-32,30-30],[31-31,32-32,31-31]]`       

=  `[[0,0,0],[0,0,0],[0,0,0]]`     is the zero matrix obtained here.

Perform the given operation on  `[[103,102,101],[102,102,100],[101,102,101]]` `-`   `[[92,92,92],[92,92,92],[92,92,92]]` ` -` `[[11,10,9],[10,10,8],[9,10,9]]`  
Solution:

These matrix are with same rows (3) and columns (3)


= `[[103-92,102-92,101-92],[102-92,102-92,100-92],[101-92,102-92,101-92]]`      ` -`     `[[11,10,9],[10,10,8],[9,10,9]]`      

=  `[[11,10,9],[10,10,8],[9,10,9]]`  - `[[11,10,9],[10,10,8],[9,10,9]]`  

= `[[0,0,0],[0,0,0],[0,0,0]]`     is the zero matrix obtained here.

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Problems to Explain "solving Zero Matrix "

Multiply this matrix  `[[93,91,91],[92,92,90]]` with the zero matrix  `[[0,0,0],[0,0,0]]`   
Solution:

It is given by    `[[93.0+91.0+91.0,93.0+91.0+91.0,93.0+91.0+91.0],[92.0+92.0+90.0,92.0+92.0+90.0,92.0+92.0+90.0]]`      

`= [[93.0+91.0+91.0,93.0+91.0+91.0,93.0+91.0+91.0],[92.0+92.0+90.0,92.0+92.0+90.0,92.0+92.0+90.0]]`     

` = [[0+0+0,0+0+0,0+0+0],[0+0+0,0+0+0,0+0+0]]`        

= `[[0,0,0],[0,0,0]]`     is the zero matrix obtained here.

Perform the subtraction operation on the matrix  `[[33,32,31],[32,32,30]]` and     `[[33,32,31],[32,32,30]]`  
Solution:

These matrix are with same rows (3) and columns (3)

= `[[33-33,32-32,31-31],[32-32,32-32,30-30]]`       

=  `[[0,0,0],[0,0,0]]`     is the zero matrix obtained here.

Perform the given operation on  `[[103,102,101],[102,102,100]]` `-`   `[[92,92,92],[92,92,92]]` ` -`   `[[11,10,9],[10,10,8]]`  
Solution:

These matrix are with same rows (3) and columns (3)


= `[[103-92,102-92,101-92],[102-92,102-92,100-92]]`      ` -`     `[[11,10,9],[10,10,8]]`      

=  `[[11,10,9],[10,10,8]]`  - `[[11,10,9],[10,10,8]]`  

= `[[0,0,0],[0,0,0]]`     is the zero matrix obtained here.