Given matrices find A - 2B and etc

Question

A= [1 -2]

     [-4 0]

B= [0 1 0]

     [-3 2 1]

C=[-1 -1]

    [0 -2]

(the brackets are actually suppose to be connected for each one)

 

(a) Find     A - 2B =

Answer:   First row=?      

                 Second row=?  

(b) Find   3A + C = 

Answer:    First row=?        

                 Second row=?  

(c)   Find     AC =

Answer:    First row=?      

                 Second row=?  

 

Answer 1

I am assuming matrix A is 2x2, matrix B is 2x3 and matrix C is 2x2.

 

If this is the case then A -2B cannot be formed because they are not the same size.

 

3A + C is found by first using scalar multiplication on A and then adding corresponding elements.

3A =[3*1 3*-2] =[3  -6]

       [3*-4 3*0]   [-12 0]

3A+C = [3+(-1) -6+(-1)]

            [-12+0   0+(-2)]

Finally 3A+C =[2    -7]

                      [-12 -2]

 

AC = [(-1)(1)+(-2)(0)  (1)(-1)+(-2)(-2)] = [-1 3]

        [(-4)(-1)+(0)(0)   (-4)(-1)+(0)(-2)]    [4  4]