Math Problem Statement
Diketahui matriks P = ( 2 1; -3 4 ), Q = ( 6 -8; 2 3 ), R = ( -1 -4; 5 4 ) dan PT adalah transpose dari matriks P, maka nilai dari 3PT - Q + 2R = ...
Solution
The given problem asks for the calculation of the expression:
where:
- is the transpose of matrix .
Steps to solve:
-
Transpose of matrix :
-
Multiply by 3:
-
Calculate :
-
Multiply matrix by 2:
-
Calculate the final result :
Thus, the final result is:
Let me know if you need more details or have further questions.
Related Questions:
- What is the formula for matrix transposition?
- How do you perform matrix multiplication by a scalar?
- Can you explain matrix addition and subtraction?
- What are some properties of matrix transposition?
- How does matrix multiplication differ from element-wise multiplication?
Tip:
Always ensure matrix dimensions match when performing addition and subtraction, as these operations are only defined for matrices of the same dimensions.
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Math Problem Analysis
Mathematical Concepts
Matrix Transposition
Matrix Scalar Multiplication
Matrix Addition
Matrix Subtraction
Formulas
Transpose of a matrix: (P^T)_ij = P_ji
Matrix scalar multiplication: c * A = c * A_ij
Matrix addition and subtraction: A ± B = (A_ij ± B_ij)
Theorems
Basic Matrix Operations
Suitable Grade Level
Grades 10-12