Let A be a m x n matrix. Recall that N(A) is the null space of A and R(A) is the column space of A (also known as the range of A ). Which of the following equalities could be FALSE? O N(A")= R(A)+ . Ο ΝA)R(AT) ., O R(A")= N(A)+ . O R(A) = N(A")t. Ο ΝA)-N(A") . O N(A):
Let A be a m x n matrix. Recall that N(A) is the null space of A and R(A) is the column space of A (also known as the range of A ). Which of the following equalities could be FALSE? O N(A")= R(A)+ . Ο ΝA)R(AT) ., O R(A")= N(A)+ . O R(A) = N(A")t. Ο ΝA)-N(A") . O N(A):
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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Question
3
Transcribed Image Text:Let A be a m x n matrix. Recall that N(A) is the null space of A and R(A) is the column
space of A (also known as the range of A ). Which of the following equalities could be FALSE?
O N(A") = R(A)t.
Ο ΝΑ) R(A") . .
O R(A") = N(A)t.
O R(A) = N(A")+.
O N(A) = N(A").
Question 6
Let A be a m × n matrix and let i be a least-squares solution to the inconsistent system
Ax = b. Which of the following statements is FALSE?
O ||b – Ax|| < ||b – Ay|| whenever Ay + Ax.
O b - Aâx 1 Ay for every y E R" .
O b – Aâ € N(A"), the null space of AT.
O x is a solution to the system AT Ax
= = ATb -
ATb; that is, AT Aây
O x is a solution to Ax
b; that is, Ax = b.
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