Linear algebra: please solve q16 and 19 correctly. Def: A matrix a is nonsinguler if the only solution to ax=0 is x=0. The matrices listed in Eq. (11) are used in some of theexercises that follow.2^-[13]· *-[23]· <-[22].A =B ==34-[-]E =D=1000100101-F = 0 3200101016. A19. AB22. F25. EF002013In Exercises 16-27, use Definition 12 to determinewhether the given matrix is singular or nonsingular. If amatrix M is singular, give all solutions of Mx = 0.17. B18. C20. BA21. D23. D + F26. DE24. E27. FT DEFINITION 12An (n × n) matrix A is nonsingular if the only solution to Ax = 0 is x = 0.Furthermore, A is said to be singular if A is not nonsingular.If A = [A₁, A2, ..., A₂], then Ax = 0 can be written asX₁A₁ + x₂A₂ + + x₂A₂ = 0,so it is an immediate consequence of Definition 12 that A is nonsingular if and only ifthe column vectors of A form a linearly independent set. This observation is importantenough to be stated as a theorem.

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Answered: The matrices listed in Eq. (11) are…

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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Linear algebra: please solve q16 and 19 correctly. Def: A matrix a is nonsinguler if the only solution to ax=0 is x=0.

The matrices listed in Eq. (11) are used in some of the
exercises that follow.
2
^-[13]· *-[23]· <-[22].
A =
B =
=
34
-[-]
E =
D=
100
010
010
1
-
F = 0 32
001
010
16. A
19. AB
22. F
25. EF
002
013
In Exercises 16-27, use Definition 12 to determine
whether the given matrix is singular or nonsingular. If a
matrix M is singular, give all solutions of Mx = 0.
17. B
18. C
20. BA
21. D
23. D + F
26. DE
24. E
27. FT

DEFINITION 12
An (n × n) matrix A is nonsingular if the only solution to Ax = 0 is x = 0.
Furthermore, A is said to be singular if A is not nonsingular.
If A = [A₁, A2, ..., A₂], then Ax = 0 can be written as
X₁A₁ + x₂A₂ + + x₂A₂ = 0,
so it is an immediate consequence of Definition 12 that A is nonsingular if and only if
the column vectors of A form a linearly independent set. This observation is important
enough to be stated as a theorem.

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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