Let's use co-factor expansion to find the determinant of this 4x4 matrix, using the column that has more zeroes in it as the co-factor, so we reduce the number of determinant calculations for the obtained sub-matrices.We pick the first column for that since it has three zeros!

Then the determinant of this matrix becomes:

$4\,*Det\left[\begin{array}{ccc}1&4&6\\0&3&8\\0&0&1\end{array}\right] +0+0+0$

And the determinant of these 3x3 matrix is very simple because most of the cross multiplications render zero:

$Det\left[\begin{array}{ccc}1&4&6\\0&3&8\\0&0&1\end{array}\right] =1 \,(3\,*\,1-0)+4\,(0-0)+6\,(0-0)=3$

Therefore, the Det of the initial matrix is : 4 * 3 = 12

and then the matrix is invertible

4 0

2 years ago

Help me out homies please

Romashka [77]

So he knows there are definitely 66 trouts as he caught and tagged them.
The next day he caught 52, but 13 of them were already tagged, so were part of the number of trout he caught before.
So he can expect that:
66+(52-13)= 105 trout are in the lake

3 0

2 years ago

Square PQRS is rotated 180° counterclockwise around the origin.

KiRa [710]

The side that is equivalent to side SR is side AB.

<h3>How to carry out Rotational Transformation?</h3>

When rotating a point 180 degrees counterclockwise about the origin, our point A(x, y) becomes A'(-x, -y). Thus, all we do is make both x and y negative.

The coordinates of the original square are;

P(2, 4); Q(5, 5); R(5, 1); S(2, 1)

Now, applying the transformation rule above gives us;

P(-2, -4); Q(-5, -5); R(-5, -1); S(-2, -1)

The side that is therefore equivalent to side SR is side AB.

Read more about Rotational Transformation at; brainly.com/question/26249005

#SPJ1

6 0

1 year ago