Chapter 16.2, Problem 8WE

To determine

To write: the value of $p$ of the scalar product.

Answer to Problem 8WE

The value of $p$ is $-30$ .

Explanation of Solution

Given information:

  $-2\left[\begin{array}{ccccc}15& -2& 0& 8& \sqrt{3}\end{array}\right]=\left[\begin{array}{ccccc}p& q& r& s& t\end{array}\right]$

Calculation: The dimensions of the given matrices are the same. Product of the corresponding elements.

  $\begin{array}{c}-2\left[\begin{array}{ccccc}15& -2& 0& 8& \sqrt{3}\end{array}\right]=\left[\begin{array}{ccccc}p& q& r& s& t\end{array}\right]\\ \left[\begin{array}{ccccc}-2\cdot 15& \left(-2\right)\cdot \left(-2\right)& -2\cdot 0& -2\cdot 8& -2\cdot \sqrt{3}\end{array}\right]=\left[\begin{array}{ccccc}p& q& r& s& t\end{array}\right]\\ \left[\begin{array}{ccccc}-30& 4& 0& -16& -2\sqrt{3}\end{array}\right]=\left[\begin{array}{ccccc}p& q& r& s& t\end{array}\right]\end{array}$

As, dimensions are equals then corresponding elements of the matrices will be equal.

Therefore, $p=-30$

So, the value of $p$ is $-30$ .