Math Problem Statement
Find the inverse of the matrix A = [[2, 3], [3, 5]].
Solution
You are asked to find the inverse of the matrix :
To find the inverse of a 2x2 matrix, we use the formula:
Where the matrix is:
For the given matrix:
Step 1: Compute the determinant of :
Step 2: Find the inverse matrix:
Using the formula, the inverse is:
Thus, the inverse of matrix is:
Let me know if you'd like further details, or have any questions. Here are some related questions you might find helpful:
- What are the properties of the inverse of a matrix?
- Can a matrix always have an inverse?
- How do you find the inverse of larger matrices (e.g., 3x3 matrices)?
- What is the determinant of a matrix and its significance?
- How is the inverse of a matrix used in solving systems of linear equations?
Tip: The inverse of a matrix exists only if its determinant is non-zero. If the determinant is zero, the matrix is called singular, and no inverse exists.
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Matrix Inversion
Determinants
Formulas
Inverse of 2x2 matrix formula: A^(-1) = 1/det(A) * [[d, -b], [-c, a]]
Determinant formula: det(A) = ad - bc
Theorems
The Inverse Matrix Theorem
Determinant and Invertibility
Suitable Grade Level
Grades 10-12