Day 2, Inverses and Derivatives of Inverses, Inverse Trig Functions
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Day 2 Inverses and Der
(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
, is the multiplicative inverse of a, because its produ
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 Linear Systems, Continued
and
The Inverse of a Matrix
Math 2
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 A , is n m matrix with
AT
ij
= Aji
rows and columns of
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 A to In. It turns out that the same sequence of row op
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 inverse to A if
AB = BA = I
where I is as usual identity mat
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 diagonal matrices with non-zero
diagonal components. In the
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 problems between
cities
Scheduling exams and assign channels
t
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, have system of equations for B3
B" #B# %B$ "
(*)
"B"
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 product is the identity
matrixwhich does nothing to a vecto
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 determinant of a 3 3 matrix can be found using the
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 nd the inverse of a 2 2 matrix, if it existed.
We will 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)
det(A)
(If det(A) = 0, A does not have an inverse).
Howe
AP-928
Streaming SIMD Extensions Inverse of 4x4 Matrix
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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 - calculating the inversemath 140 the inverse of a 3inverse of a 3
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 us to write the solution of the system using the inverse