1•Linear equations, linear functions•Engineering (physical) interpretation of linear equations•Fundamental linear algebra operations in MATLAB•Problem of inversion•DeterminantsIi(t i)Lecture 8: Linear Algebra•Inversion (square matrices)•Independence of vectors•Range of a matrix•Null space of a matrixLinear equationsExample of linear equations (Chap. 6, p. 365)Which can be written in matrix formOr more symbolically as:WhereLinear equationsLinear equations: Can be written in matrix form:Or alternatively in compact formExample of linear equationsLinear circuitEquations for voltages and intensities are linearIn 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’sWhat is a linear function?Letbe a function. It is said to be linear if This is sometimes called superpositionMatrix representation of a linear function
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