Math Problem Statement
find the inverse of the following matrix using row operation method 2 -3 3 A= 2 2 3 3 -2 2
Solution
To find the inverse of the given matrix using row operations, follow these steps:
Given matrix:
We augment with the identity matrix :
Now, perform row operations to convert the left side into the identity matrix.
Step 1: Make the first pivot 1
Divide row 1 by 2:
Step 2: Make other elements in column 1 zero
Subtract from and from :
Step 3: Make the second pivot 1
Divide row 2 by 5:
Step 4: Make other elements in column 2 zero
Subtract from and add to :
Step 5: Make the third pivot 1
Divide row 3 by -2.5:
Step 6: Make other elements in column 3 zero
Subtract from :
Thus, the inverse of is:
Would you like a verification step to ensure correctness?
Related Questions
- How do you check if a matrix is invertible before finding its inverse?
- What are alternative methods to find the inverse of a matrix?
- Can you find the determinant of to confirm its invertibility?
- How does the row operation method compare to the adjoint method?
- What are some real-world applications of matrix inversion?
Tip:
Always check the determinant before attempting inversion; if , the matrix is singular and has no inverse.
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Math Problem Analysis
Mathematical Concepts
Matrix Algebra
Row Operations
Inverse of a Matrix
Formulas
Matrix Inverse using Row Operations
Identity Matrix Augmentation
Theorems
Inverse of a Matrix
Row Reduction Method
Suitable Grade Level
Grades 11-12