Answer: The required matrix A is
![A=\left[\begin{array}{ccc}0&0&0\\0&0&0\\4&0&0\\0&4&0\\0&0&4\end{array}\right]_{5\times3} .](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%260%260%5C%5C0%260%260%5C%5C4%260%260%5C%5C0%264%260%5C%5C0%260%264%5Cend%7Barray%7D%5Cright%5D_%7B5%5Ctimes3%7D%20.)
Step-by-step explanation: We are given the following linear transformation :

We are to find the matrix A relative to the bases
and 
We have

Therefore, the matrix A is of order 5 × 3, given by
![A=\left[\begin{array}{ccc}0&0&0\\0&0&0\\4&0&0\\0&4&0\\0&0&4\end{array}\right]_{5\times3} .](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%260%260%5C%5C0%260%260%5C%5C4%260%260%5C%5C0%264%260%5C%5C0%260%264%5Cend%7Barray%7D%5Cright%5D_%7B5%5Ctimes3%7D%20.)
Thus, the required matrix A is
![A=\left[\begin{array}{ccc}0&0&0\\0&0&0\\4&0&0\\0&4&0\\0&0&4\end{array}\right]_{5\times3} .](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%260%260%5C%5C0%260%260%5C%5C4%260%260%5C%5C0%264%260%5C%5C0%260%264%5Cend%7Barray%7D%5Cright%5D_%7B5%5Ctimes3%7D%20.)
Answer:
Inspect the graph to see if any vertical line drawn would intersect the curve more than once. If there is any such line, the graph does not represent a function. If no vertical line can intersect the curve more than once, the graph does represent a function.
Step-by-step explanation:
<h3>
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You have to calculate the probability that it lands on 4. There are 2 possibilities from the 8 that it lands on 4. So the chance is 2/8, which is the same as 4/16
<span>Declaring the volume function
double PyramidVolume(double baseLength, double baseWidth, double pyramidHeight){
double baseArea = baseLength * baseWidth;
double vol = ((baseArea * pyramidHeight) * 1/3);
return vol;
}
int main() {
cout << "Volume for 1.0, 1.0, 1.0 is: " << PyramidVolume(1.0, 1.0, 1.0) << endl;
return 0;
}
Defining the function,
include <iostream>
double PyramidVolume(double, double, double);
int main()
{
std::cout << "Volume for 1.0, 1.0, 1.0 is: " << PyramidVolume(1.0, 1.0, 1.0) << std::endl;
return 0;
}
double PyramidVolume(double length, double width, double height)
{
return length * width * height / 3;
}</span>