Math Problem Statement
Hasil perkalian matriks (2, -3; 0, 5; -1, 3) dengan (0, 3; -4, 1) dan invers dari matriks (-4, 2; -5, 3)
Solution
The image contains two questions about matrix operations:
Question 3:
- Problem: Calculate the product of two matrices: 2 & -3 \\ 0 & 5 \\ -1 & 3 \end{pmatrix} \times \begin{pmatrix} 0 & 3 \\ -4 & 1 \end{pmatrix}$$
- Solution: I'll compute the matrix multiplication step by step.
Question 4:
- Problem: Find the inverse of matrix , where: -4 & 2 \\ -5 & 3 \end{pmatrix}$$
- Solution: I'll compute the inverse using the formula for the inverse of a 2x2 matrix.
Let me solve both questions.### Solutions:
Question 3:
The result of the matrix multiplication:
2 & -3 \\ 0 & 5 \\ -1 & 3 \end{pmatrix} \times \begin{pmatrix} 0 & 3 \\ -4 & 1 \end{pmatrix} = \begin{pmatrix} 12 & 3 \\ -20 & 5 \\ -12 & 0 \end{pmatrix}$$ #### Question 4: The inverse of matrix $$A$$, where: $$A = \begin{pmatrix} -4 & 2 \\ -5 & 3 \end{pmatrix}$$ is: $$A^{-1} = \begin{pmatrix} -1.5 & 1 \\ -2.5 & 2 \end{pmatrix}$$ Would you like more details or have any questions about these calculations? Here are 5 related questions you can explore: 1. How is matrix multiplication defined for arbitrary-sized matrices? 2. How can you check if a matrix is invertible? 3. What are the conditions for a matrix to have an inverse? 4. How would the product of two matrices change if one matrix is not invertible? 5. What role does the determinant play in calculating the inverse of a matrix? **Tip**: For a 2x2 matrix, the inverse can be calculated if the determinant is non-zero, and it follows the formula: $$A^{-1} = \frac{1}{\text{det}(A)} \begin{pmatrix} d & -b \\ -c & a \end{pmatrix}$$ for $$A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}$$.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Matrix Multiplication
Matrix Inversion
Formulas
Matrix multiplication formula: (AB)ij = Σ Aik * Bkj
Inverse of a 2x2 matrix: A^{-1} = 1/det(A) * (d, -b; -c, a)
Theorems
Matrix multiplication
Inverse of a matrix requires a non-zero determinant
Suitable Grade Level
Grades 10-12