SOLUTION: <pre> a = [ 6 5] [-5 -5] and b = [ 5 0] [-5 -1] a. a + b b. 5a c. 3a - 2b d. ab</pre>

 a = [ 6  5]
     [-5 -5] 

and 

b = [ 5   0]
    [-5  -1]

a. a + b

[ 6  5]     [ 5   0]    [ 6+5   5+0]   [ 11   5]
[-5 -5]  +  [-5  -1]  = [-5-5  -5-1] = [-10  -6]  



b. 5a

  [ 6  5]   [ 5×6   5×5]   [ 30   25]
5×[-5 -5] = [5×-5  5×-5] = [-25  -25] 

c. 
         
3a - 2b = 

  [ 6  5]       [ 5   0]    [ 3×6   3×5]   [ 2×5   2×0]    
3×[-5 -5]  -  2×[-5  -1]  = [3×-5  3×-5] - [2×-5  2×-1] =  

 
[ 18  15]   [ 10  0]   [    18-10      15-0]   [ 18-10   15-0]  
[-15 -15] - [-10 -2] = [-15-(-10)  -15-(-2)] = [-15+10  -15+2] =

[ 8  15]
[-5 -13]

d. ab

[ 6  5] [ 5   0]    [     6×5+5×(-5)       6×0+5×(-1)]   [30-25  0-5]
[-5 -5]×[-5  -1]  = [(-5)×5+(-5)(-5)  (-5)×0+(-5)(-1)] = [-25+25 0+5] =

[5  -5]  
[0   5]

Edwin

To add matrices, add their elements in each cell.  

    Do it cell by cell, for each and every cell.




To subtract matrices, subtract their elements in each cell.  

    Do it cell by cell, for each and every cell.




To multiply a matrix by a number, multiply each element of the matrix in its cell by the number.

    Do it cell by cell, for each and every cell.