Question

The matrix product
$\begin{bmatrix}a\\ b\\ c\end{bmatrix} \times\begin{bmatrix}x&y&z\end{bmatrix} \times\begin{bmatrix}p\\ q\\ r\end{bmatrix}$ equals :

• A. $\frac{pqr - abc}{xyz}$
• B. $\frac{xyz . pqr }{abc}$
• C. $\frac{pqr . abc}{xyz}$
• D. none of these

Answer 1

Answer: (D)

Matrix product is shown below
$\begin{bmatrix}a\\ b\\ c\end{bmatrix} \times [x \ y \ z]\times\begin{bmatrix}p\\ q\\ r\end{bmatrix} = \begin{bmatrix}ax&ay&az\\ bx&by&bz\\ cx&cy&cz\end{bmatrix}\times\begin{bmatrix}p\\ q\\ r\end{bmatrix}$
$ =\begin{bmatrix}a\left(xp+yq+zr\right)\\ b\left(xp+yq+zr\right)\\ c\left(xp+yq+zr\right)\end{bmatrix}=\left(xp+yq+zr\right)\begin{bmatrix}a\\ b\\ c\end{bmatrix}$