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DETERMINANT. definition and origin. Associated with every square matrix A there is a number called the determinant of A. The definition of the determinant of a 2 2 matrix follows:. = ad - bc. det. Associated with every square matrix A there is - PowerPoint PPT Presentation
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DETERMINANT
definition
and
origin
Associated with every square matrix A there is a number called the determinant of A.The definition of the determinant of a 22 matrix follows:
(a c
)b ddet = ad - bc
Associated with every square matrix A there is a number called the determinant of A.The definition of the determinant of a 22 matrix follows:
(a c
)b ddet = ad - bc
Associated with every square matrix A there is a number called the determinant of A.The definition of the determinant of a 22 matrix follows:
(a c
)b ddet = ad - bc
The concept “determinant” arose from early attempts to generalize the process of solving systems of linear equations.Consider the following:
kdybx
jcyaxsystemtheSolve
:
ckdjdk
cjbjak
kb
jabcad
db
ca
detdetdet
kdybx
jcyaxsystemtheSolve
:
ckdjdk
cjbjak
kb
jabcad
db
ca
detdetdet
kdybx
jcyaxsystemtheSolve
:
dk
cj
kb
ja
db
ca
replace y coordinates with j
k
replace x coordinates with j
k
ckdjdk
cjbjak
kb
jabcad
db
ca
detdetdet
kdybx
jcyaxsystemtheSolve
:
)(
)(:for
kdybxa
jcyaxbysolveto
kdybx
jcyax
ckdjdk
cjbjak
kb
jabcad
db
ca
detdetdet
kdybx
jcyaxsystemtheSolve
:
)(
)(:for
kdybxa
jcyaxbysolveto
kdybx
jcyax
ckdjdk
cjbjak
kb
jabcad
db
ca
detdetdet
bcad
bjaky
bjakybcad
akadyabx
bjbcyabx
)(
kdybx
jcyaxsystemtheSolve
:
)(
)(:for
kdybxa
jcyaxbysolveto
kdybx
jcyax
ckdjdk
cjbjak
kb
jabcad
db
ca
detdetdet
bcad
bjaky
bjakybcad
akadyabx
bjbcyabx
)(
kdybx
jcyaxsystemtheSolve
:
)(
)(:for
kdybxc
jcyaxdxsolveto
kdybx
jcyax
ckdjdk
cjbjak
kb
jabcad
db
ca
detdetdet
kdybx
jcyaxsystemtheSolve
:
)(
)(:for
kdybxc
jcyaxdxsolveto
kdybx
jcyax
ckdjdk
cjbjak
kb
jabcad
db
ca
detdetdet
bcad
ckdjy
ckdjxbcad
ckcdybcx
djcdyadx
)(
kdybx
jcyaxsystemtheSolve
:
)(
)(:for
kdybxc
jcyaxdxsolveto
kdybx
jcyax
ckdjdk
cjbjak
kb
jabcad
db
ca
detdetdet
bcad
ckdjy
ckdjxbcad
ckcdybcx
djcdyadx
)(
kdybx
jcyaxsystemtheSolve
:
The following presentation entitled
will outline the algorithm for evaluating the determinant of a 33 matrix
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