Math Problem Statement
hitung invers matriks a jika invers tersebut ada
hitung invers matriks a jika invers tersebut ada
Solution
The determinant of matrix is approximately . Since the determinant is not zero, the inverse of the matrix exists. I'll now calculate the inverse of matrix .The inverse of matrix is:
0.5283 & -0.4717 & 0.0755 & 0.0377 \\ -0.2547 & 0.2453 & -0.1792 & 0.1604 \\ -0.4481 & 0.3019 & 0.2217 & -0.0142 \\ 0.2311 & -0.0189 & 0.0330 & -0.1085 \end{pmatrix}$$ Let me know if you'd like a detailed breakdown of the calculation. Would you like any further explanation or clarification? Here are 5 related questions to expand on this topic: 1. How is the determinant of a matrix used to check for invertibility? 2. What are some methods to compute the inverse of a matrix manually? 3. Can any square matrix always have an inverse? 4. How do row operations relate to finding the inverse of a matrix? 5. What are some applications of matrix inverses in real-world problems? **Tip**: When calculating the inverse manually, row-reduction (Gaussian elimination) is an effective method, but it can be tedious for large matrices.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Matrix Inversion
Linear Algebra
Determinants
Formulas
Determinant of a matrix: det(A)
Inverse of a matrix: A^{-1} = 1/det(A) * adj(A)
Theorems
A square matrix is invertible if and only if its determinant is non-zero.
Suitable Grade Level
College level (Advanced Linear Algebra)