Question: Let A be the n x n matrix with 0's on the main diagonal, and 1's everywhere else. For an arbitrary vector in , solve the linear system , expressing the components of in terms of the components of . See Exercise 69 for the case n=3 .
The solution of the linear system is .
If A is an n x m matrix with row vectors and is a vector in Rm then, .
Consider the linear system.
The matrix form of the system is,
The solution is, .
Consider the linear system, of in terms of the components of .
The solution, .
Hence, is the solution of the linear system
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