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lecture_E7_Linear_Algebra_6p

lecture_E7_Linear_Algebra_6p - Lecture 8 Linear Algebra...

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1 Linear equations, linear functions Engineering (physical) interpretation of linear equations Fundamental linear algebra operations in MATLAB Problem of inversion Determinants I i ( t i ) Lecture 8: Linear Algebra Inversion (square matrices) Independence of vectors Range of a matrix 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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