Math Tutoring on Determining Inverse Matrices
If A is an (m x n) matrix, then ImA = A and AIn = A.
If A is an (n x n) square matrix, then AIn = InA = A.
Now if A is an (n x n) invertible matrix such that AB = BA = In, then B is the inverse of A and is denoted by A-1.
We need to remember that, not all matrices have an inverse.
We can determine Inverse Matrices during math tutoring in two steps:
1) Create an augmented matrix in the form [A|In].
2) Perform row matrix operations resulting in an augmented matrix in the form [In|A-1].
The main idea here is to convert A into In on the left side of the augmented matrix. The right side will become A-1.
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1. What is the role of Identity Matrix in finding Inverse Matrix?
2. What is Augmented Matrix?
3. Define Invertible Matrix.
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