To solve the following system of linear equations using inverse matrix
Answer to Problem 43E
Explanation of Solution
Given:
Concept used:
To find inverse of a square matrix A, following steps should be followed.
- Augment given matrix with the identity matrix
- Perform row operations to make the identity matrix to the left and the right matrix becomes inverse matrix.
In this way, inverse matrix of a matrix can be obtained.
Formula used:
Calculation:
Consider given system of equations,
Writing above system of linear equations in matrix form
Here,
Now, find the inverse matrix of matrix A.
Step 1: Augmenting matrix A with the identity matrix
Step 2: Performing row operations to make the identity matrix to the left.
So, inverse matrix is,
Now, applying the formula
Finding the solutions,
Conclusion:
Therefore, the solution to given system of equations is
Chapter 8 Solutions
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