The test was repeated on three more groups of 50 patients​ each, with the results summarized in the following matrices. Find the total results for all 200 patients.
left bracket Start 2 By 2 Matrix 1st Row 1st Column 20 2nd Column 5 2nd Row 1st Column 5 2nd Column 20 EndMatrix right bracket
   left bracket Start 2 By 2 Matrix 1st Row 1st Column 22 2nd Column 3 2nd Row 1st Column 8 2nd Column 17 EndMatrix right bracket
   left bracket Start 2 By 2 Matrix 1st Row 1st Column 23 2nd Column 2 2nd Row 1st Column 2 2nd Column 23 EndMatrix right bracket
 
The matrix summarizing the results for all 200 patients is 
  
enter your response here. ​(Simplify your​ answer.)

To find the total results for all 200 patients, we need to add the three given matrices element by element. Let’s break down the process:

Given matrices:

\[
A = \begin{bmatrix} 20 & 5 \\ 5 & 20 \end{bmatrix}
\quad
B = \begin{bmatrix} 22 & 3 \\ 8 & 17 \end{bmatrix}
\quad
C = \begin{bmatrix} 23 & 2 \\ 2 & 23 \end{bmatrix}
\]

We now add the matrices:

\[
A + B + C = \begin{bmatrix} 20 + 22 + 23 & 5 + 3 + 2 \\ 5 + 8 + 2 & 20 + 17 + 23 \end{bmatrix}
\]

Perform the addition:

\[
= \begin{bmatrix} 65 & 10 \\ 15 & 60 \end{bmatrix}
\]

Thus, the matrix summarizing the results for all 200 patients is:

\[
\boxed{\begin{bmatrix} 65 & 10 \\ 15 & 60 \end{bmatrix}}
\]

This is the simplified result. Would you like more details on matrix addition, or do you have any other questions?

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Here are 5 related questions you might find interesting:
1. What are the properties of matrix addition?
2. How does matrix multiplication differ from matrix addition?
3. How are matrices applied in medical statistics?
4. What happens when you add matrices of different dimensions?
5. How can matrix operations be applied in data analysis?

**Tip:** Always ensure the matrices are of the same dimension before performing addition.

The test was repeated on three more groups of 50 patients each, with the results summarized in the following matrices. Find the total results for all 200 patients. Left bracket Start 2 By 2 Matrix 1st Row 1st Column 20 2nd Column 5 2nd Row 1st Column 5 2nd Column 20 EndMatrix right bracket left bracket Start 2 By 2 Matrix 1st Row 1st Column 22 2nd Column 3 2nd Row 1st Column 8 2nd Column 17 EndMatrix right bracket left bracket Start 2 By 2 Matrix 1st Row 1st Column 23 2nd Column 2 2nd Row 1st Column 2 2nd Column 23 EndMatrix right bracket

This problem demonstrates how to add matrices by summarizing the test results from multiple groups of patients. Learn how to perform element-wise matrix addition, a key concept in linear algebra. The total results for all 200 patients are calculated step by step. Suitable for students in Grades 9-12.

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