Solution Found!
[M] Suppose memory or size restrictions prevent a matrix
Chapter 2, Problem 27E(choose chapter or problem)
[M] Suppose memory or size restrictions prevent a matrix program from working with matrices having more than 32 rows and 32 columns, and suppose some project involves 50 × 50 matrices A and B. Describe the commands or operations of the matrix program that accomplish the following tasks.a. Compute A + B.b. Compute AB.c. Solve Ax = b for some vector b in ?50, assuming that A can be partitioned into a 2 × 2 block matrix [Ai j], with A11 an invertible 20 × 20 matrix, A22 an invertible 30 × 30 matrix, and A12 a zero matrix. [Hint: Describe appropriate smaller systems to solve, without using any matrix inverses.]
Questions & Answers
QUESTION:
[M] Suppose memory or size restrictions prevent a matrix program from working with matrices having more than 32 rows and 32 columns, and suppose some project involves 50 × 50 matrices A and B. Describe the commands or operations of the matrix program that accomplish the following tasks.a. Compute A + B.b. Compute AB.c. Solve Ax = b for some vector b in ?50, assuming that A can be partitioned into a 2 × 2 block matrix [Ai j], with A11 an invertible 20 × 20 matrix, A22 an invertible 30 × 30 matrix, and A12 a zero matrix. [Hint: Describe appropriate smaller systems to solve, without using any matrix inverses.]
ANSWER:Solution 27E(a)Use the MAPLE software, to compute the matrix: .First, upload the linear algebra package, by giving the Maple command:with(linalg):C11:=submatrix(A, 1 .. 30, 1 .. 30)+submatrix(B, 1 .. 30, 1 .. 30);C12:=submatrix(A, 1 .. 30, 31 .. 50)+submatrix(B, 1 .. 30, 31 .. 50);C21:=sub