Question: An n Ã n matrix A is called block diagonal if it can be partitioned in such a way that all the nonzero entries are

An n Ã— n matrix A is called block diagonal if it can be partitioned in such a way that all the nonzero entries are contained in square blocks Aij.
(a) Partition the following matrix into a block diagonal matrix:

(b) If A is block diagonal, then the linear system Ax = b is said to be uncoupled, because it can be solved by considering the linear systems with coefficient matrices An and right sides an appropriate portion of b. Solve Ax = b by "uncoupling" the linear system when A is the 4 Ã— 4 matrix of part (a) and

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