Math Problem Statement
Solve 37 only
Determine whether matrix A is invertible, and if so, find the inverse for the matrix A = [[1, 0, 1], [1, 1, 0], [0, 1, 1]].
Solution
The matrix from problem 37 is invertible since its determinant is , which is not zero.
The inverse of matrix is:
0.5 & 0.5 & -0.5 \\ -0.5 & 0.5 & 0.5 \\ 0.5 & -0.5 & 0.5 \end{bmatrix}$$ Would you like further details on how the inverse was computed or have any questions? Here are 5 related questions to expand your understanding: 1. How can you check if a matrix is invertible without calculating the determinant? 2. What is the geometric significance of the determinant of a matrix? 3. Can you find the inverse of a 2x2 matrix manually? If so, how? 4. Why does a determinant of 0 indicate that a matrix is not invertible? 5. What are some applications of matrix inverses in real-world problems? **Tip**: When a matrix has a determinant of 0, it is called singular, meaning it cannot be inverted.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Matrix Inverses
Determinants
Formulas
AX = I
Determinant formula for a 3x3 matrix
Theorems
Invertible Matrix Theorem
Determinant properties
Suitable Grade Level
Grades 11-12, University-level linear algebra