The order of the matrix product left[ {x,y,z} | vedclass

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(B) Let the given matrices be $A = [x \, y \, z]$,$B = \begin{bmatrix} a & h & g \ h & b & f \ g & f & c \end{bmatrix}$,and $C = \begin{bmatrix} x \

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$1 	imes 1$

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(B) Let the given matrices be $A = [x \, y \, z]$,$B = \begin{bmatrix} a & h & g \ h & b & f \ g & f & c \end{bmatrix}$,and $C = \begin{bmatrix} x \ y \ z \end{bmatrix}$.The order of matrix $A$ is $1 	imes 3$.The order of matrix $B$ is $3 	imes 3$.The order of matrix $C$ is $3 	imes 1$.First,we calculate the product $AB$. Since the number of columns in $A$ $(3)$ equals the number of rows in $B$ $(3)$,the product $AB$ is defined and its order is $1 	imes 3$.Next,we calculate the product $(AB)C$. Since the number of columns in $(AB)$ $(3)$ equals the number of rows in $C$ $(3)$,the product is defined.The resulting order is $(1 	imes 3) 	imes (3 	imes 1) = 1 	imes 1$.

The order of the matrix product $\left[ {x\,y\,z} \right]\,\left[ {\begin{array}{{20}{c}} a&h&g\\ h&b&f\\ g&f&c \end{array}} \right]\,\left[ {\begin{array}{{20}{c}} x\\ y\\ z \end{array}} \right]$ is:

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The order of the matrix product $\left[ {x\,y\,z} \right]\,\left[ {\begin{array}{*{20}{c}} a&h&g\\ h&b&f\\ g&f&c \end{array}} \right]\,\left[ {\begin{array}{*{20}{c}} x\\ y\\ z \end{array}} \right]$ is: