The volume of a cylinder is the area of the base times the height
area of the base: 3.14*4² (diameter is 8, so radius is 4)
height: 20
3.14*4²*20=1004.8
60% of 1004.8=602.88

5 0

3 years ago

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Consider the matrix <img src="https://tex.z-dn.net/?f=A_%7B4x4%7D%2C%20det%28A%29%20%3D%20-2" id="TexFormula1" title="A_{4x4}, d

Lerok [7]

We found a counterexample, so the statement is false.

<h3>Is the statement true?</h3>

Let's use the matrix:

$\left[\begin{array}{cccc}-2&0&0&0\\0&1&0&0\\0&0&1&0\\ 0&0&0&1 \end{array}\right]$

This is a 4x4 matrix with determinant equal to -2.

The inverse matrix is:

$\left[\begin{array}{cccc}1/2&0&0&0\\0&-1&0&0\\0&0&-1&0\\ 0&0&0&-1 \end{array}\right]$

If we multiply it by 2, we get:

$\left[\begin{array}{cccc}1&0&0&0\\0&-2&0&0\\0&0&-2&0\\ 0&0&0&-2 \end{array}\right]$

The adjoint of that is the original matrix, actually:

$\left[\begin{array}{cccc}-2&0&0&0\\0&1&0&0\\0&0&1&0\\ 0&0&0&1 \end{array}\right]$

Which we already know, has a determinant of -2.

So the statement is false, as we found a counterexample.

If you want to learn more about matrices:

brainly.com/question/11989522

#SPJ1

7 0

2 years ago