https://file.aiquickdraw.com/mathbot/file/172585530691001e13kwv.jpg

diketahui matriks beserta ukurannya yaitu A 3x4 , B 3x4, C 4x2, D 3x2, dan E 4x3 tentukan manakah yang dapat dilakukan, jika tidak dapat dilakukan beri komentar

Based on the image and the provided matrices:

- \( A \) is a \( 3 \times 4 \) matrix.
- \( B \) is a \( 3 \times 4 \) matrix.
- \( C \) is a \( 4 \times 2 \) matrix.
- \( D \) is a \( 3 \times 2 \) matrix.
- \( E \) is a \( 4 \times 3 \) matrix.

The expressions given are:

1. \( AE + B \)
2. \( AB + B \)
3. \( A E^T A \)
4. \( AD^T + E^T D \)

### Checking Validity:

1. **\( AE + B \):**
   - \( AE \): \( A \) is \( 3 \times 4 \) and \( E \) is \( 4 \times 3 \), so \( AE \) results in a \( 3 \times 3 \) matrix.
   - \( B \) is \( 3 \times 4 \).
   - The matrices \( AE \) and \( B \) have different sizes, so the addition cannot be performed.
   - **Not possible**.

2. **\( AB + B \):**
   - \( AB \): \( A \) is \( 3 \times 4 \) and \( B \) is \( 3 \times 4 \). Matrix multiplication requires the inner dimensions to match, but they don't (4 ≠ 3).
   - Therefore, \( AB \) is **not defined**, and hence the addition is also not possible.
   - **Not possible**.

3. **\( A E^T A \):**
   - \( E^T \) is the transpose of \( E \), so \( E^T \) is \( 3 \times 4 \).
   - \( AE^T \): \( A \) is \( 3 \times 4 \) and \( E^T \) is \( 3 \times 4 \). Their inner dimensions don't match (4 ≠ 3), so \( AE^T \) is **not defined**.
   - Therefore, \( AE^T A \) is also not possible.
   - **Not possible**.

4. **\( AD^T + E^T D \):**
   - \( D^T \) is the transpose of \( D \), so \( D^T \) is \( 2 \times 3 \).
   - \( AD^T \): \( A \) is \( 3 \times 4 \) and \( D^T \) is \( 2 \times 3 \). Their inner dimensions don't match (4 ≠ 2), so \( AD^T \) is **not defined**.
   - Similarly, \( E^T D \): \( E^T \) is \( 3 \times 4 \) and \( D \) is \( 3 \times 2 \). Their inner dimensions don't match (4 ≠ 3), so \( E^T D \) is **not defined**.
   - Hence, the expression \( AD^T + E^T D \) is not possible.
   - **Not possible**.

### Conclusion:

None of the given expressions can be performed due to mismatched matrix dimensions or undefined operations.

Would you like a more detailed explanation on matrix operations or any specific point? Here are some relative questions that could expand your understanding:



Diketahui matriks beserta ukurannya yaitu A 3x4 , B 3x4, C 4x2, D 3x2, dan E 4x3 tentukan manakah yang dapat dilakukan, jika tidak dapat dilakukan beri komentar

Analyze whether matrix operations can be performed on matrices A (3x4), B (3x4), C (4x2), D (3x2), and E (4x3). This problem covers matrix multiplication and addition concepts, suitable for Grades 11-12 students.

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