Consider the matrices A = begin{bmatrix} 4 & | vedclass

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(C) The dimensions of the matrices are: $A$ is $3 	imes 3$,$B$ is $3 	imes 2$,and $C$ is $3 	imes 1$.$(i) (AB)^T C$: $AB$ is $(3 	imes 3)(3 	imes

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exactly three are defined

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(C) The dimensions of the matrices are: $A$ is $3 	imes 3$,$B$ is $3 	imes 2$,and $C$ is $3 	imes 1$.$(i) (AB)^T C$: $AB$ is $(3 	imes 3)(3 	imes 2) = 3 	imes 2$. Thus,$(AB)^T$ is $2 	imes 3$. The product $(2 	imes 3)(3 	imes 1)$ is defined.$(ii) C^T C (AB)^T$: $C^T$ is $1 	imes 3$ and $C$ is $3 	imes 1$,so $C^T C$ is $1 	imes 1$. $(AB)^T$ is $2 	imes 3$. The product $(1 	imes 1)(2 	imes 3)$ is not defined because the number of columns in the first matrix $(1)$ does not equal the number of rows in the second matrix $(2)$.$(iii) C^T AB$: $C^T$ is $1 	imes 3$ and $AB$ is $3 	imes 2$. The product $(1 	imes 3)(3 	imes 2)$ is defined.$(iv) A^T AB B^T C$: $A^T$ is $3 	imes 3$,$AB$ is $3 	imes 2$,$B^T$ is $2 	imes 3$,and $C$ is $3 	imes 1$. The product $(3 	imes 3)(3 	imes 2)(2 	imes 3)(3 	imes 1)$ is defined.Thus,$(i), (iii),$ and $(iv)$ are defined. Exactly three are defined.

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