help me please (please make sure if you write the formula in latex etc. it wont show math input error; i couldnt read my former question explanation bc of the math input error. thanks) Prove that for any m × n matrix A and vector b = Rm, the vector AT6 belongs to the image of matrixAT A. (This would prove that the normal equation AT Ax ATb always has a solution, and, therefore, aleast squares solution of Ax = b always exists.) Hint: use the resultker(ATA) =ker(A), and the Fundamental Theorem of Linear Algebra.=

The Fundamental Theorem of Linear Algebra states that for any matrix A :The null space of A is…

Prove that for any m x n matrix A and vector b € Rm, the vector ATb belongs to the image of matrix AT A. (This would prove that the normal equation AT Ax = ATb always has a solution, and, therefore, a least squares solution of Ax=b always exists.) Hint: use the result ker(ATA) = ker(A), and the Fundamental Theorem of Linear Algebra.

Prove that for any m x n matrix A and vector b € Rm, the vector ATb belongs to the image of matrix AT A. (This would prove that the normal equation AT Ax = ATb always has a solution, and, therefore, a least squares solution of Ax=b always exists.) Hint: use the result ker(ATA) = ker(A), and the Fundamental Theorem of Linear Algebra.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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