Explain where this system of equations came from and what it means. (Think about

Question

Explain where this system of equations came from and what it means. (Think about what the left hand side and the right hand side of each equation mean.)

Let us denote the column vector (pF, pT, pC, pCM , pSB)T by p, and let C be the coefficient matrix of the above system. We can now rewrite that system as

Cp = p

or equivalently

Cp - p = Cp - Ip = (C - I)p = 0

where I is the 5x5 matrix with 1's on the diagonal and 0's everywhere else. The property of the matrix I we are using is that Iv = v for any vector v.

Explanation / Answer

This system of equations describes the incomes and expenses of each person in Matrixville. On the left side, we have expenses, and on the right we have income. The income should be equal to the expenses because it is a closed system and no money can leave. The expenses are then distributed to the incomes of the other citizens.

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.