1
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Linear equations, linear functions
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Engineering (physical) interpretation of linear equations
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Fundamental linear algebra operations in MATLAB
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Problem of inversion
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Determinants
I
i
(
t i
)
Lecture 8: Linear Algebra
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Inversion (square matrices)
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Independence of vectors
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Range of a matrix
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Null space of a matrix
Linear equations
Example of linear equations (Chap. 6, p. 365)
Which can be written in matrix form
Or more symbolically as:
Where
Linear equations
Linear equations:
Can be written in matrix form:
Or alternatively in compact form
Example of linear equations
Linear circuit
Equations for voltages and
intensities are linear
In the following equation, if you know the voltages, the intensities
can be obtained by solving the following linear system
where the unknown are the currents i’s
What is a linear function?
Let
be a function. It is said to be linear if
This is sometimes called superposition
Matrix representation of a linear function

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