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Step 2 Now use elementary row operations on the entire matrix $\begin{bmatrix} A & : & I \end{bmatrix}$ to row reduce A to I. If this is possible, the resultant matrix is $\begin{bmatrix} I & : & A^{-1} \end{bmatrix}$ where $A^{-1}$ is the inverse of A. Perform a row operation to make the first entry in the second row equal to zero. $\begin{bmatrix} 1 & 1 & : & 1 & 0 \\ 0 & 1 & : & -4 & 1 \end{bmatrix}$

          Step 2
Now use elementary row operations on the entire matrix $\begin{bmatrix} A & : & I \end{bmatrix}$ to row reduce A to I. If this is possible, the resultant matrix is $\begin{bmatrix} I & : & A^{-1} \end{bmatrix}$ where $A^{-1}$ is the inverse of A. Perform a row operation to make the first entry in the second row equal to zero.
$\begin{bmatrix} 1 & 1 & : & 1 & 0 \\ 0 & 1 & : & -4 & 1 \end{bmatrix}$

Step 2
Now use elementary row operations on the entire matrix < b m a t r i x > to row reduce A to I. If this is possible, the resultant matrix is < b m a t r i x > where A^-1 is the inverse of A. Perform a row operation to make the first entry in the second row equal to zero.
< b m a t r i x >

Added by Jamie C.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Allison Knapp

Step 1

First, we need to know the matrix A and the augmented matrix [A: 1]. Let's assume A is a 2x2 matrix: A = $\begin{bmatrix} a & b \\ c & d \end{bmatrix}$ The augmented matrix [A: 1] will be: [A: 1] = $\begin{bmatrix} a & b & 1 & 0 \\ c & d & 0 & 1 \end{bmatrix}$ Show more…

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Now use elementary row operations on the entire matrix [A: 1] to row reduce A to I. If this is possible, the resultant matrix is li : A-1| where A-1 is the inverse of A: Perform a row operation to make the first entry in the second row equal to zero. X R1 + R2 ~ Step