Answer:
a. AB: 3 by 7
b. BA: N by N
c. A^TB: N by N
d. BC: 6 by 3
Step-by-step explanation:
Given
[tex]A =3\ by\ 6[/tex]
[tex]B =6\ by\ 7[/tex]
[tex]C =7\ by\ 3[/tex]
Required
The dimension of the following matrices
As a general rule:
For A * B to be successful, the columns in a must equal the rows in B
Using this rule, we have:
[tex]A_{m*n} * B_{n * p} = AB_{m*p}[/tex]
So:
[tex](a)\ AB[/tex]
[tex]A_{3*6} * B_{6*7} \to AB_{3 * 7}[/tex]
[tex](b)\ BA[/tex]
[tex]B_{6*7} * A_{3*6} \to AB_{N * N}[/tex]
The column numbers of B does not equal the row numbers of A.
Hence, BA does not exist
[tex](c)\ A^TB[/tex]
[tex]A^T[/tex] implies that:
If [tex]A =3\ by\ 6[/tex], then
[tex]A^T = 6\ by\ 3[/tex]
So:
[tex]A^T_{6*3} * B_{6,7} \to A^TB_{N*N}[/tex]
The column numbers of A^T does not equal the row numbers of B.
Hence, [tex]A^TB[/tex] does not exist
[tex](d)\ BC[/tex]
[tex]B_{6*7} * C_{7*3} \to BC_{6,3}[/tex]
