Linear algebra: please q8 and 10.Equations 9 and 10 are above The (2 x2) matrices listed in Eq. (9) are used in severalof the exercises that follow.A2113]-2 3c=[2³]1 101[83]z = [88]BExercises 1-6 refer to the matrices in Eq. (9).1. Find (a) A + B; (b) A + C; (c) 6B; and (d) B+ 3C.2. Find (a) B+C; (b) 3A; (c) A +2C; and (d) C+8Z.3. Find a matrix D such that A + D = B.4. Find a matrix D such that A + 2D = C.5. Find a matrix D such that A + 2B + 2D = 3B.6. Find a matrix D such that 2A +5B+D=2B+3A.9. a) Arb) Brc) C(s + 3t)The vectors listed in Eq. (10) are used in several of theexercises that follow.12r=--[!] -[3]-[4] --[-]-4t =In Exercises 7-12, perform the indicated computation,using the vectors in Eq. (10) and the matrices in Eq. (9).7. a) r + s8. a) t+sb) 2r + tc) 2s + ub) r +3uc) 2u + 3t10. a) Bt(10)b) C(r + s)c) B(r +s)

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Answered: The (2 x 2) matrices listed in Eq. (9)…

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 q8 and 10. Equations 9 and 10 are above

The (2 x2) matrices listed in Eq. (9) are used in several
of the exercises that follow.
A
21
13
]
-2 3
c=[2³]
1 1
0
1
[83]
z = [88]
B
Exercises 1-6 refer to the matrices in Eq. (9).
1. Find (a) A + B; (b) A + C; (c) 6B; and (d) B+ 3C.
2. Find (a) B+C; (b) 3A; (c) A +2C; and (d) C+8Z.
3. Find a matrix D such that A + D = B.
4. Find a matrix D such that A + 2D = C.
5. Find a matrix D such that A + 2B + 2D = 3B.
6. Find a matrix D such that 2A +5B+D=2B+3A.
9. a) Ar
b) Br
c) C(s + 3t)
The vectors listed in Eq. (10) are used in several of the
exercises that follow.
1
2
r=
--[!] -[3]
-[4] --[-]
-4
t =
In Exercises 7-12, perform the indicated computation,
using the vectors in Eq. (10) and the matrices in Eq. (9).
7. a) r + s
8. a) t+s
b) 2r + t
c) 2s + u
b) r +3u
c) 2u + 3t
10. a) Bt
(10)
b) C(r + s)
c) B(r +s)

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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