(a) Suppose that Ax = b is a consistent linear system, and that p is a solution of it. Prove that every solution of Ax = b can be written as x = p + z where z € null(A). (b) Let A be an m x n matrix, and let B be an n × p matrix. Prove that (AB)T = BT AT.

(a) Suppose that Ax = b is a consistent linear system, and that p is a solution of it. Prove that every solution of Ax = b can be written as x = p + z where z € null(A). (b) Let A be an m x n matrix, and let B be an n × p matrix. Prove that (AB)T = BT AT.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter10: Matrices

Section10.5: Eigenvalues And Eigenvectors

Problem 13E

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1.
(a) Suppose that Ax = b is a consistent linear system, and that p is a solution of it. Prove that every
solution of Ax = b can be written as x = p + z where z = null(A).
(b) Let A be an m × n matrix, and let B be an n × p matrix. Prove that (AB)T = BT AT.

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