Unformatted text preview: Example
Demonstrate the theorem for 2 × 4 matrices:
A= a11 a12 a13 a14
a21 a22 a23 a24 Theorem
If A is an n × n matrix and R is the row-reduced echelon form of
A, then either R contains a row of zeros or R = In . Outline Identity Matrices The Inverse of a Matrix Deﬁnition
Let A be an n × n matrix.
1 An n × n matrix B satisfying
AB = In and BA = In is called an inverse of A.
2 If A has an inverse, we say that A is invertible. 3 If A is not invertible, we say A is singular. Inverse of a Matrix Outline Identity Matrices Inverse of a Matrix Examples Example
1 Show that B is an inverse of A, where
A= 2 1 −2
5 and B = Show that the matrix: 123
A= 4 5 6 000
is singular. −5 −2
−3 −1 Outline Identity Matrices Inverse of a Matrix Uniqueness of Inverses
If A is an n × n matrix, and both B and C are inverses of A, then
B = C ....
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