need help for this in matlab form 6 If A B and C are arbitr

? need help for this in matlab form

6. If [A], [B] and [C] are arbitrary rectangular matrices, it can be shown that when the matrix multiplication [A][B][C] exists, then Using MAMA B, (a) Construct rectangular matrices of minimum size 3 that [A][B][C] is defined. (b) Compute required matrix multiplications. (c) Find reduced row echelon forms. (d) Comment on the rank of matrices and verify the given relation. Notes: 1 In MATLAB , matrix multiplications can be performed using * operator i.e. [A][B]= [A] * [B]. To obtain reduced row echelon form of a matrix, use \'rref()\' function. Gauss-Jordan method, which is a variant of standard Gauss elimination, is utilized in `rref()\'. The function returns to reduced row echelon form not row echelon form! 3 Although rank of a matrix can be calculated directly with `rank()\' function, you are asked to find reduced row echelon forms.

Solution

>> A=[1,2,3;2,3,4;4,5,6;5,6,7]

A =

1 2 3
2 3 4
4 5 6
5 6 7

>> B=[7,8,9,10;5,6,7,8;2,4,6,8]

B =

7 8 9 10
5 6 7 8
2 4 6 8

>> C=[1,0,5;2,6,8;8,5,2;1,2,9]

C =

1 0 5
2 6 8
8 5 2
1 2 9

>> D=A*B

D =

23 32 41 50
37 50 63 76
65 86 107 128
79 104 129 154

>> E=B*C

E =

105 113 207
81 87 159
66 70 126

>> F=A*B*C

F =

465 497 903
717 767 1395
1221 1307 2379
1473 1577 2871

>> rref(D)

ans =

1 0 -1 -2
0 1 2 3
0 0 0 0
0 0 0 0

>> rref(E)

ans =

1.0000 0 -2.3333
0 1.0000 4.0000
0 0 0

>> rref(F)

ans =

1.0000 0 -2.3333
0 1.0000 4.0000
0 0 0
0 0 0

>> rref(B)

ans =

1 0 -1 -2
0 1 2 3
0 0 0 0

from the above, we can say that

rank(AB)=2 rank(BC)=2 rank(B)=2 and rank(ABC)=2

there fore

rank(AB)+rank(BC)=2+2 = 4

rank(B)+rank(ABC)=2+2 = 4

so in this case

rank(AB) + rank(BC) = rank(B) + rank(ABC)

so the given statement is correct.