
To show: The inverse of the matrix

Answer to Problem 89AYU
The inverse of the matrix
Explanation of Solution
Given information:
A
Calculation:
Consider the
The inverse of the matrix,
Let the inverse of the matrix be
Using the relation,
Now, multiplying the above two matrices, we get,
Now, we equate the corresponding elements of the two matrices. First we write the system of equations when equated to the first column and when system of equations when equated to the second column.
Combing the above two matrices such that the identity matrix is on the right hand side, we get,
Now, we apply the Gauss-Jordan elimination to find the inverse of
First we have to make the entry
Next, we have to make the entry
Next, we have to make the entry
Next, we have to make the entry
Therefore, the inverse of the matrix
Rewrite it as,
Here, determinant is
Thus, it is shown that the inverse of the matrix
Chapter 11 Solutions
Precalculus
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