For each of the following equations, perform the following tasks: Decide if the equation is mathematically true for the variable values provided below. Implement the equations in MATLAB, and test if they are true in the floating point arithmetic withinMATLAB for the variable values provided. (For example, the equation 3 + 72 = 5 in matlab would correspond to the command disp(3+7^2==5) and yields, upon execution of the command, the value 0 corresponding to false. This is expected since the equation is not mathematically true.) Where the MATLAB result differs from the mathematical expectation explain in one or more full sentences why the MATLAB results are different. The equations to be considered are, with z = 10^-12, y = 1, 1. z^2 + z = z 2. z + z^3 = z 3. z^3 = 0 4. -1 + z^2 = -1 - z^2 5. (z - y)(z + y) = z^2 - y^2 6. (z - y)(z + y) = z^2 7. (z - y)(z + y) = -y^2
For each of the following equations, perform the following tasks:
Decide if the equation is mathematically true for the variable values provided below.
Implement the equations in MATLAB, and test if they are true in the floating point arithmetic withinMATLAB for the variable values provided. (For example, the equation 3 + 72 = 5 in matlab would correspond to the command disp(3+7^2==5) and yields, upon execution of the command, the value 0 corresponding to false. This is expected
since the equation is not mathematically true.)
Where the MATLAB result differs from the mathematical expectation explain in one or more full sentences why the MATLAB results are different.
The equations to be considered are, with z = 10^-12, y = 1,
1. z^2 + z = z
2. z + z^3 = z
3. z^3 = 0
4. -1 + z^2 = -1 - z^2
5. (z - y)(z + y) = z^2 - y^2
6. (z - y)(z + y) = z^2
7. (z - y)(z + y) = -y^2
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