Question

Determine whether the statements that follow are true or false, and justify your answer.

18:$\left[\begin{array}{ccc}11& 13& 15\\ 17& 19& 21\end{array}\right]\left[\begin{array}{c}-1\\ 3\\ -1\end{array}\right]\mathbf{=}\left[\begin{array}{c}13\\ 19\\ 21\end{array}\right]$

Short answer

False, because the product of $\left[\begin{array}{ccc}11& 13& 15\\ 17& 19& 21\end{array}\right]\left[\begin{array}{c}-1\\ 3\\ -1\end{array}\right]$is $\left[\begin{array}{c}13\\ 19\end{array}\right]$, which is not same as the given product.

Step-by-step solution

Step 1:Simplification of matrix

We have given the equation of matrix which is $\left[\begin{array}{ccc}11& 13& 15\\ 17& 19& 21\end{array}\right]\left[\begin{array}{c}-1\\ 3\\ -1\end{array}\right]=\left[\begin{array}{c}13\\ 19\\ 21\end{array}\right]$.

Here, first matrix is of order$2\times 3$. And second matrix is of order $3\times 1$ .

Then, the product of these matrixes will give matrix of order $2\times 1$.

Justification of answer

The product of the matrix will be

$\left[\begin{array}{ccc}11& 13& 15\\ 17& 19& 21\end{array}\right]\left[\begin{array}{c}-1\\ 3\\ -1\end{array}\right]=\left[\begin{array}{c}-11+39-15\\ -17+57-21\end{array}\right]=\left[\begin{array}{c}13\\ 19\end{array}\right]$

Hence, the product of matrix$\left[\begin{array}{ccc}11& 13& 15\\ 17& 19& 21\end{array}\right]\left[\begin{array}{c}-1\\ 3\\ -1\end{array}\right]=\left[\begin{array}{c}13\\ 19\\ 21\end{array}\right]$, which is not same as the given product, so the given statement is false.