Certainly! Let's break down each part of the problem step-by-step, based on the given data:
1. Evaluate the components of the matrix:
- For the element [tex]\(2 \sqrt{100}\)[/tex]:
[tex]\[
2 \sqrt{100} = 2 \times 10 = 20
\][/tex]
- For the element [tex]\(3 / 256\)[/tex]:
[tex]\[
\frac{3}{256} \approx 0.01171875
\][/tex]
2. Construct the matrix with these evaluated elements:
[tex]\[
\begin{bmatrix}
1900 & 20 & 0.01171875 \\
-557 & 150 & -145 \\
& \pm 200 &
\end{bmatrix}
\][/tex]
Here, [tex]\(\pm 200\)[/tex] suggests a symmetric value around zero, which we'll denote simply as [tex]\(200\)[/tex].
3. Evaluate the division operations:
- For [tex]\(\frac{4}{67}\)[/tex]:
[tex]\[
\frac{4}{67} \approx 0.05970149253731343
\][/tex]
- For [tex]\(\frac{5}{97428}\)[/tex]:
[tex]\[
\frac{5}{97428} \approx 0.0000513199490906105
\][/tex]
4. Evaluate the summation:
[tex]\[
34 + 25 = 59
\][/tex]
5. Collecting the results:
- The matrix after evaluation:
[tex]\[
\begin{bmatrix}
1900 & 20 & 0.01171875 \\
-557 & 150 & -145 \\
& 200 &
\end{bmatrix}
\][/tex]
- The results of the division operations:
[tex]\[
0.05970149253731343 \quad \text{and} \quad 0.0000513199490906105
\][/tex]
- Summation result:
[tex]\[
59
\][/tex]
- Given results:
[tex]\[
6.432 \quad \text{and} \quad 112
\][/tex]
Combining all these, we have our final results:
- [tex]\(2 \sqrt{100} = 20\)[/tex]
- [tex]\(3 / 256 \approx 0.01171875\)[/tex]
- [tex]\(\frac{4}{67} \approx 0.05970149253731343\)[/tex]
- [tex]\(\frac{5}{97428} \approx 0.0000513199490906105\)[/tex]
- Summation of [tex]\(34 + 25 = 59\)[/tex]
- Matrix:
[tex]\[
\begin{bmatrix}
1900 & 20 & 0.01171875 \\
-557 & 150 & -145 \\
& 200 &
\end{bmatrix}
\][/tex]
- Final given values:
[tex]\[
6.432 \quad \text{and} \quad 112
\][/tex]
Thus, each operation is evaluated as shown, providing the comprehensive and detailed solution required.
