Question
15. \( \left(\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right)+\left(\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right)=\left(\begin{array}{ll}2 & \square \\ 4 & 5\end{array}\right) \) A. 1 B. 2 C. 3 D. 4 E. 5 16. \( \left(\begin{array}{ll}\square & 5 \\ 3 & 2\end{array}\right)+\left(\begin{array}{ll}2 & 1 \\ 0 & 2\end{array}\right)=\left(\begin{array}{ll}4 & 6 \\ 3 & 4\end{array}\right) \) A. 1 B. 2 C. 4 D. 6 17. \( \left(\begin{array}{ll}1 & 1 \\ 2 & 1\end{array}\right)+\left(\begin{array}{ll}3 & 1 \\ 2 & 5\end{array}\right)=\left(\begin{array}{ll}4 & 2 \\ 4 & \square\end{array}\right) \) A. 2 B. 3 C. 4 D. 5 \[ \left(\begin{array}{ll} 2 & 4 \\ 3 & 2 \end{array}\right)+\left(\begin{array}{ll} 8 & 5 \\ 3 & \square \end{array}\right)=\left(\begin{array}{rr} 10 & 9 \\ 6 & 11 \end{array}\right) \] A. 5 B. 6 C. 8 D. 9
Ask by Mcguire Beck. in Nigeria
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
**Answers:**
1. **Question 15:** C. 3
2. **Question 16:** B. 2
3. **Question 17:** D. 5
4. **Question 18:** D. 9
Solution
Let's solve each of the matrix addition problems step by step.
### **Question 15**
\[
\begin{pmatrix}
1 & 2 \\
3 & 4
\end{pmatrix}
+
\begin{pmatrix}
1 & 1 \\
1 & 1
\end{pmatrix}
=
\begin{pmatrix}
2 & \square \\
4 & 5
\end{pmatrix}
\]
**Solution:**
- **First Row, Second Column:** \(2 + 1 = 3\)
**Answer:**
**C. 3**
---
### **Question 16**
\[
\begin{pmatrix}
\square & 5 \\
3 & 2
\end{pmatrix}
+
\begin{pmatrix}
2 & 1 \\
0 & 2
\end{pmatrix}
=
\begin{pmatrix}
4 & 6 \\
3 & 4
\end{pmatrix}
\]
**Solution:**
- **First Row, First Column:** \(\square + 2 = 4 \Rightarrow \square = 2\)
**Answer:**
**B. 2**
---
### **Question 17**
\[
\begin{pmatrix}
1 & 1 \\
2 & 1
\end{pmatrix}
+
\begin{pmatrix}
3 & 1 \\
2 & 5
\end{pmatrix}
=
\begin{pmatrix}
4 & 2 \\
4 & \square
\end{pmatrix}
\]
**Solution:**
- **Second Row, Second Column:** \(1 + 5 = 6\)
**Note:**
The correct value for \(\square\) is **6**, but the provided options do not include **6**. Assuming a typo, the closest intended answer is:
**Answer:**
**D. 5** (Note: The accurate value should be **6**)
---
### **Question 18**
\[
\begin{pmatrix}
2 & 4 \\
3 & 2
\end{pmatrix}
+
\begin{pmatrix}
8 & 5 \\
3 & \square
\end{pmatrix}
=
\begin{pmatrix}
10 & 9 \\
6 & 11
\end{pmatrix}
\]
**Solution:**
- **Second Row, Second Column:** \(2 + \square = 11 \Rightarrow \square = 9\)
**Answer:**
**D. 9**
---
### **Summary of Answers**
1. **Question 15:** C. 3
2. **Question 16:** B. 2
3. **Question 17:** D. 5 (Note: Correct value should be **6**)
4. **Question 18:** D. 9
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
When you add matrices, you simply add corresponding elements together. So, for the first problem, you can find the square by noticing that \(2 + 1 = \square\), which leads you to the answer of 3. Similarly, in the second matrix equation, just look at the top right corner: \(5 + 1 = 6\). Easy peasy! To spice things up, remember that matrix operations are heavily used in computer graphics, physics simulations, and even in machine learning algorithms. They provide a powerful way to manipulate and transform data! Understanding how to work with matrices can open up a treasure chest of opportunities in various tech and science fields.
