a +c a) Let S = {[a – b] |a, b E R}. Find three vectors in R° so that each vector in s b-a can be written as a linear combination of the three vectors. Are these vectors linearly independent? Justify your answer. 1 2 -2 1 -1 01. Determine whether the rows of A are linearly 1 b) Let A = [! 2 4 -5 4 -2 -4 4 -1 independent. Evaluate | – 2A2| and |3A-11.

a +c a) Let S = {[a – b] |a, b E R}. Find three vectors in R° so that each vector in s b-a can be written as a linear combination of the three vectors. Are these vectors linearly independent? Justify your answer. 1 2 -2 1 -1 01. Determine whether the rows of A are linearly 1 b) Let A = [! 2 4 -5 4 -2 -4 4 -1 independent. Evaluate | – 2A2| and |3A-11.

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

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a +c
a) Let S = {[a – b] |a, b € R}. Find three vectors in R3 so that each vector in S
b – a
can be written as a linear combination of the three vectors. Are these vectors
linearly independent? Justify your answer.
1
2
-2
1
1
-1
b) Let A = [1
"J. Determine whether the rows of A are linearly
2
4
-5
4
-2 -4
4
-1
independent. Evaluate | - 242| and |3A-1|.

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