Math Problem Statement
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
Solution
Based on the image and the provided matrices:
- is a matrix.
- is a matrix.
- is a matrix.
- is a matrix.
- is a matrix.
The expressions given are:
Checking Validity:
-
:
- : is and is , so results in a matrix.
- is .
- The matrices and have different sizes, so the addition cannot be performed.
- Not possible.
-
:
- : is and is . Matrix multiplication requires the inner dimensions to match, but they don't (4 ≠ 3).
- Therefore, is not defined, and hence the addition is also not possible.
- Not possible.
-
:
- is the transpose of , so is .
- : is and is . Their inner dimensions don't match (4 ≠ 3), so is not defined.
- Therefore, is also not possible.
- Not possible.
-
:
- is the transpose of , so is .
- : is and is . Their inner dimensions don't match (4 ≠ 2), so is not defined.
- Similarly, : is and is . Their inner dimensions don't match (4 ≠ 3), so is not defined.
- Hence, the expression is not possible.
- Not possible.
Conclusion:
None of the given expressions can be performed due to mismatched matrix dimensions or undefined operations.
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Math Problem Analysis
Mathematical Concepts
Matrix Multiplication
Matrix Addition
Linear Algebra
Formulas
Matrix multiplication: For matrices A (m×n) and B (n×p), the product AB is a matrix of size m×p
Matrix transpose: The transpose of a matrix E (m×n) is a matrix of size n×m
Theorems
Matrix multiplication is defined when the number of columns in the first matrix matches the number of rows in the second matrix
Suitable Grade Level
Grades 11-12