If AT A is an invertible matrix, then which of the following is trueA has linearly independent columnsA has linearly dependent columnsI.II.II.Axb has only one least square solution.IV.AAT = I(a) Only I(b) I & III(c) II & III(d) I, III & IV (e) All of theseO aO ePo

If ATA is an ivertible matrix, then which of the following is true I. A has linearly independent columns A has linearly dependent columns b has only one least II. III. Ax %3D square solution. IV. AAT (a) Only I (b) I & III (c) II & III (d) I, III & IV (e) All of these O a O d O e

If ATA is an ivertible matrix, then which of the following is true I. A has linearly independent columns A has linearly dependent columns b has only one least II. III. Ax %3D square solution. IV. AAT (a) Only I (b) I & III (c) II & III (d) I, III & IV (e) All of these O a O d O e

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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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

If AT A is an invertible matrix, then which of the following is true
A has linearly independent columns
A has linearly dependent columns
I.
II.
II.
Ax
b has only one least square solution.
IV.
AAT = I
(a) Only I
(b) I & III
(c) II & III
(d) I, III & IV (e) All of these
O a
O e
Po

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