[a+a) Let S =bERFind three vectors in R so that each vector- ain S can be written as a linear combination of the three vectors. Are thesevectors linearly independent? Justify your answer.1-211Let A1-1Determine whether the rows of A are44-5-2-44-1.linearly independent. Evaluate |– 242| and 13A 11. [1-1][1B = |23[2-1Let A3.0 and C =|11.11-1..1-2]Lo3a) Eind A-1, if exists.b) If possible, find the matrix X such that AX + B = C.c) If possible, find a matrix Y such that YA +B = C.

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[a+c] a) Let S = Find three vectors in R³ so that each vector a - b а, b - a in S can be written as a linear combination of the three vectors, Are these vectors linearly independent? Justify your answer.

[a+c] a) Let S = Find three vectors in R³ so that each vector a - b а, b - a in S can be written as a linear combination of the three vectors, Are these vectors linearly independent? Justify your answer.

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

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[a+
a) Let S =
bER
Find three vectors in R so that each vector
- a
in S can be written as a linear combination of the three vectors. Are these
vectors linearly independent? Justify your answer.
1
-2
1
1
Let A
1
-1
Determine whether the rows of A are
4
4
-5
-2
-4
4
-1.
linearly independent. Evaluate |– 242| and 13A 11.

[1
-1]
[1
B = |2
3
[2
-1
Let A
3.
0 and C =|1
1
.1
1
-1.
.1
-2]
Lo
3
a) Eind A-1, if exists.
b) If possible, find the matrix X such that AX + B = C.
c) If possible, find a matrix Y such that YA +B = C.

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