illusiia

## Answered question

2021-09-22

We need to find the volume of the parallelepiped with only one vertex at the origin and conterminous vertices at .

### Answer & Explanation

mhalmantus

Skilled2021-09-23Added 105 answers

So, u can setup the matrix A, where the columns are the vectors given.
$A=\left[\begin{array}{ccc}1& -2& -1\\ 3& 0& 3\\ 0& 2& -1\end{array}\right]$
The volume of the parallelepiped is equal to the absolute value of the determinant of A.
Volume $=|det\left(A\right)|$
And lets calculate the determinant. Expanding along the first column gives us to shown computation.
$A=|\begin{array}{ccc}1& -2& -1\\ 3& 0& 3\\ 0& 2& -1\end{array}|=|\begin{array}{cc}0& 3\\ 2& -1\end{array}|-3|\begin{array}{cc}-2& -1\\ 2& -1\end{array}|+0|\begin{array}{cc}-2& -1\\ 0& 3\end{array}|=-6-12=-18$
Now, we know that the volume of the parallelepiped is 18.
Results: Volume is 18.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?