Suppose a, b and c are 2 ×2 matrices , e, f and g are 3 × 3 matrices, h and k are 2×3 matrices and l and m are 3×2 matrices. for each of the following, if the operation is denied, specify the size of the matix that results. (a) ab+c (b) 3gf (c) ck+b (d) ck+h (e) emc (f) glh (g) hlg (h) 2el+5mb

a) 2x2 b)3x3 c) Not possible d) 2x3 e) 3x2 f) 3x3 g)Not possible h)3x2

Step-by-step explanation:

-> we can only add matrices with same size

-> we can only multiply when columns of first equal to rows of second

-> nxm multiplied by pxq gives nxq eg 3x2 mul 2x2 gives 3x2

-> addition and mul by const number dont change the size

So considering the above facts :-

a) AB+C = [(2x2)(2X2)]+(2x2)=(2x2)+(2x2)=2x2

b) 3GF =3[(3x3)(3x3)]=3(3x3)=3x3

c)CK+B= [(2x2)(2x3)]+(2x2)=(2x3)+(2x2) which is not possible (see point 1)

d)CK+H =as CK is (2x3) so (2x3)+(2x3)=(2x3)

e)EMC=[(3x3)(3x2)](2x2)=(3x2)(2x2)=3x3

f)GLH=[(3x3)(3x2)](2x3)=(3x2)(2x3)=3x3

g)HLG=[(2x3)(3x2)](3x3)=(2x2)(3x3)= not possible(see point 2)

h)2EL+5MB=2[(3x3)(3x2)]+5[(3x2)(2x2)]=(3x2)+(3x2)=3x2