Question

What is the order of the product $\left[\begin{array}{ccc}x& y& z\end{array}\right]\left[\begin{array}{ccc}a& h& g\\ h& b& f\\ g& f& c\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]$ ?

• A. $3\times 1$
• B. $1\times 1$
• C. $1\times 3$
• D. $3\times 3$

Answer 1

The correct option is B $1\times 1$

If two matrix of order $x\times m$ and $m\times n$ are multiplied then the order of resultant matrix is $x\times n$.

Now in the given equation going from left, matrices of order $1\times 3$ and $3\times 3$ are multiplied. So, the order of resultant matrix is $1\times 3$

And now this is multiplied by matrix of order $3\times 1$. This will give resultant matrix of order $1\times 1$

Hence, B is correct.