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Introduction to Linear Algebra

Exercise 2.7.29

Answers

(a): Total currents are $A^{T} y = [\begin{matrix} 1 & 0 & 1 \\ - 1 & 1 & 0 \\ 0 & - 1 & - 1 \end{matrix}] [\begin{matrix} y_{BC} \\ y_{CS} \\ y_{BS} \end{matrix}] = [\begin{matrix} y_{BC} + y_{BS} \\ - y_{BC} + y_{CS} \\ - y_{CS} - y_{BS} \end{matrix}]$
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(b): Either way ${(Ax)}^{T} y = x^{T} (A^{T} y) = x_{B} y_{BC} + x_{B} y_{BS} - x_{C} y_{BC} + x_{C} y_{CS} - x_{S} y_{CS} - x_{S} y_{BS} .$
Six terms.

mathchakra

2022-01-16 12:41

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