QUESTION 10IfAx = bis an inconsistent linear system, thenATAX = ATbis also inconsistent.O TrueO False

Answered: Image /qna-images/answer/77eea139-da02-48f6-9e82-da70c1e007b6.jpg

Answered: QUESTION 10 If Ax=b is an inconsistent…

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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Consider the following. u = 7i+ 6j, v = 5i + 8j (a) Find the projection of u onto v. 415 89 -i + 664 j 89 (b) Find the vector component of u orthogonal to v. -21 118 i+ 65 65
Is the following system of equation consistent? If so, determine which variables are free variables in the system of linear equation. X1 + 3x2 - 2x3 + 2x5 = 0 2x1 + 6x2 - 5x3 - 2x4 +4x5 = -1 5x3 + 10x4 = 5 %3D Ox 4 consistent Ox_1 Ox_3 O not consistent Ox 2 x_5
Select T if the statement is true (in all cases), or select F if false (for at least one example).
1. True or False? Justify all answers. a. A system of 4 linear equations in 3 unknowns has no solutions. True or False, Justify the answer. b. There exist three planes in R³ which intersect in exactly three points. True or False, Justify the answer. c. If u, v and w are linearly dependent, then w can be written as linear combination of u and v. True or False, Justify the answer. d. Let A be a 4 x 5 matrix. Then the column vectors of A are linearly dependent. True or False, Justify the answer. e. f. If u is in span{v, w} then u is in span{v + w, w - v}. True or False, Justify the answer. let A, B be two matrices. If (A - B)² = A² - 2AB + B², then AB = BA. True or False, Justify the answer. g. If A and B are symmetric matrices, then AB is a symmetric matrix. True or False, Justify the answer.
Prove that the following statement is FALSE: A system of four linear equations in three unknowns is always inconsistent. Proof idea: Start by recalling that inconsistent means that there is no solution. Now write down a specific example of a system of four equations in variables x1, x2, x3 that WILL have a solution. Hint: Show that it does have a solution.
33 please
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QUESTION 10 If Ax=b is an inconsistent linear system, then ATAx=A¹b is also inconsistent. O True O False