Question

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

• A. $\left[\begin{array}{ccc}ax+hy+gz& h+b+f& g+f+c\end{array}\right]$
• B. $\left[\begin{array}{ccc}a& h& g\\ hx& by& fz\\ g& f& c\end{array}\right]$
• C. $\left[\begin{array}{ccc}ax& hy& gz\\ hx& by& fz\\ gx& fy& cz\end{array}\right]$
• D. $\left[\begin{array}{ccc}ax+hy+gz& hx+by+fz& gx+fy+cz\end{array}\right]$

Answer 1

Answer: (D)

$\left[\begin{array}{ccc}ax+hy+gz& hx+by+fz& gx+fy+cz\end{array}\right]$

Order of matrix $\left[\begin{array}{ccc}x& y& z\end{array}\right]$ is $(1\times 2)$

Order of matrix $\left[\begin{array}{ccc}a& h& g\\ h& b& f\\ g& f& c\end{array}\right]$ is $(3\times 3)$

So, 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}{ccc}ax+hy+gz& hx+by+fz& gx+fy+cz\end{array}\right]$