Consider the matrices
`A=[(4,6,-1),(3,0,2),(1,-2,5)], B=[(2,4),(0,1),(-1,2)], C=[(3),(1),(2)]`
Out of the given matrix products, which one is not defined ?

Options

A. `(AB)^(T)C`
B. `C^(T)C (AB)^(T)`
C. `C^(T)AB`
D. `A^(T)AB B^(T)C`

Answer

B

Explanation

`A rarr 3xx3, B rarr 3xx2, C rarr 3xx1`
`AB rarr 3xx2 implies (AB)^(T)=2xx3 implies (AB)^(T)C` is defined
`C^(T) rarr 1xx3, implies C^(T) C rarr 1xx1`
Hence `C^(T)C(AB)^(T)` is not defined. Now, `C^(T) AB` is also defined.
`A^(T) rarr 3xx3, B^(T) rarr 2xx3`
`A^(T)A rarr 3xx3`
`B B^(T) rarr 3xx3`
`implies A^(T) AB B^(T) rarr 3xx3`
`implies A^(T) AB B^(T) C` is defined