Day 2, Inverses and Derivatives of Inverses, Inverse Trig Functions
Wednesday, September 01, 2010
12:43 PM
Day 2 Inverses and Derivs, Invtrig Page 1
Day 2 Inverses and Derivs, Invtrig Page 2
Day 2 Inv
(Section 8.3: The Inverse of a Square Matrix) 8.47
SECTION 8.3: THE INVERSE OF A SQUARE MATRIX
PART A: (REVIEW) THE INVERSE OF A REAL NUMBER
1
If a is a nonzero real number, then aa 1 = a = 1 .
a
1
Solving Linear
Systems
Math 240
Solving Linear
Systems
Gauss-Jordan
elimination
Rank
Inverse
matrices
Denition
Computing
inverses
Properties of
inverses
Using inverse
matrices
Conclusion
Solving Linea
Lecture 2
Matrix Operations
transpose, sum & dierence, scalar multiplication
matrix multiplication, matrix-vector product
matrix inverse
21
Matrix transpose
transpose of m n matrix A, denoted AT or
Math 160 Discussion Notes
Brian Powers TA Fall 2011
2.5 The Gauss-Jordan Method of finding an inverse
Say we have matrix A, and a sequence of Row elementary row operations E1, E2, Ek which will
reduce
Lecture 12.
Inverse matrix .
To be read to the music of
Back To You by Bryan Adams
1
DEFINITION OF INVERSE MATRIX
Definition. Let A is a square matrix. Some matrix B (if it exists)
is said to be inver
Lecture 7: Definition of an Inverse Matrix
and Examples
In the previous lecture we gave examples of pairs of nxn matrices whose products
were the identity matrix: the elementary matrices and the diago
Graph Theory
Chapter 8
Varying Applications (examples)
Computer networks
Distinguish between two chemical
compounds with the same molecular
formula but different structures
Solve shortest path problem
Inverse and Elementary Matrices
1. Inverse matrices
Recall the economy problem:
B" total production of coal
B# total production of steel
B$ total production of electricity
Based on an economic model,
81
2.5. Inverse Matrices
2.5 Inverse Matrices
Suppose A is a square matrix. We look for an inverse matrix A 1 of the same size, such
that A 1 times A equals I . Whatever A does, A 1 undoes. Their prod
Determinants & Inverse Matrices
The determinant of the 2 2 matrix
a b
c d
is the number ad cb.
The above sentence is abbreviated as
a b
det
= ad
c d
Example.
4
det
1
2
3
= 4( 3)
cb
1( 2) =
12 + 2 =
10
The inverse of a n n matrix
Jackie Nicholas
Mathematics Learning Centre
University of Sydney
c 2010 University of Sydney
The n n case
In the previous module we dened an inverse matrix and saw how
to n
Section 4.3 : The Inverse of a 3 3 Matrix
For any n n matrix the adjoint and determinant are dened and satisfy
A adj(A) = adj(A) A = det(A) In
Provided det(A) = 0, A is invertible and
A1 =
1
adj(A)
d
AP-928
Streaming SIMD Extensions Inverse of 4x4 Matrix
March 1999
Order Number: 245043-001
Information in this document is provided in connection with Intel products. No license, express or implied, b
math 140 - calculating the inverse of a 3 3 matrix.
math 140 - calculating the inverse of a
Find the inverse of
1 1
A = 0 2
2 3
3x3 matrix inverseFind the inverse of
1
1
0
1 1
0 2
th 140 - calculati
Solution by
Inverse Matrix Method
8.2
Introduction
The power of matrix algebra is seen in the representation of a system of simultaneous linear equations
as a matrix equation. Matrix algebra allows u