Question

Find the determinant for the 3 by 3 matrix given. Consider the determinant.

Answer 1

The determinant of the matrix given is -49

Explanation:

We are given determinant
`\left|\begin{array}{ccc}4&2&-1\\3&0&4\\-3&1&1\end{array}\right|`

The determinant can be found as follows

`4\left|\begin{array}{cc}0&4\\1&1\\\end{array}\right|-2\left|\begin{array}{cc}3&4\\-3&1\\\end{array}\right|-1\left|\begin{array}{cc}3&0\\-3&1\\\end{array}\right|`

Now solving:

`4(0-4)-2(3+12)-1(3+0)\\=4(-4)-2(15)-1(3)\\=-16-30-3\\=-49`

So, determinant of the matrix given is -49