The set of 2 x 3 matrices M2x3 with standard matrix operations is a vector space. Task Select all sets that are subspace of M2x3 221 +12+ 2z3 – 274 + I5 – 316 = 221 - 12- I3 – 3z4 – 3z5 + 2z6 = 1 (I1 I I3 1. 211 – 312 + I3 + z5 I3 + 215 - Z6 -321 – 3z2 + 273 – 14 + 2z5 – 216 = 1 I4 I5 I6 -1 -1 -272 - 14 + 2z5 – 376 -Iz +I3 - 2z4 + 2z6 -11 + 2z2 – 3z3 - 274 + 2z5 = 0 (I1 I I3 211 + 2z2 – 2z3 – 2z4 + 2z5 +2z6 %3D 2. 271 +12+ I3 - 14 + 2z5 – I6 = 271 – 3z3 – 374 – 2z5 – I6 -z1 + 2z2 + 2z3 + 2z4 + I6 -1 1 %3D -1 3. | 271 + z2 - 3z3 +14- Is - I6 IS {(: 4. |-271 – 313 - I4 – 3z5 I5 I1- 213 - 314– Is +16 %3D 5. || -321 +12 - 213 – 374 – 316 = 0 I5 -3z1 - 12- I3+2z4 + 2zs %3D Iz + 2z3 – 14 – 2z5 = | -271 + 12 - Ia + 2zs + I6 -3z3 - 274 – Is + 216 6. %3D I5 1. 1. Il || ||
The set of 2 x 3 matrices M2x3 with standard matrix operations is a vector space. Task Select all sets that are subspace of M2x3 221 +12+ 2z3 – 274 + I5 – 316 = 221 - 12- I3 – 3z4 – 3z5 + 2z6 = 1 (I1 I I3 1. 211 – 312 + I3 + z5 I3 + 215 - Z6 -321 – 3z2 + 273 – 14 + 2z5 – 216 = 1 I4 I5 I6 -1 -1 -272 - 14 + 2z5 – 376 -Iz +I3 - 2z4 + 2z6 -11 + 2z2 – 3z3 - 274 + 2z5 = 0 (I1 I I3 211 + 2z2 – 2z3 – 2z4 + 2z5 +2z6 %3D 2. 271 +12+ I3 - 14 + 2z5 – I6 = 271 – 3z3 – 374 – 2z5 – I6 -z1 + 2z2 + 2z3 + 2z4 + I6 -1 1 %3D -1 3. | 271 + z2 - 3z3 +14- Is - I6 IS {(: 4. |-271 – 313 - I4 – 3z5 I5 I1- 213 - 314– Is +16 %3D 5. || -321 +12 - 213 – 374 – 316 = 0 I5 -3z1 - 12- I3+2z4 + 2zs %3D Iz + 2z3 – 14 – 2z5 = | -271 + 12 - Ia + 2zs + I6 -3z3 - 274 – Is + 216 6. %3D I5 1. 1. Il || ||
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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Hi. Can you solve this with explanation? I am beginner in algebra .
Transcribed Image Text:The set of 2 x 3 matrices M2x3 with standard matrix operations is a vector space.
Task
Select all sets that are subspace of M2x3
-214 + I5 -
2x1 - 12 - I3 – 374 – 3z5 + 2x6
211 - 312 + I3 + I5
211 + 12 + 23
3z6
-1
1
1
1.
-1
Is + 215 - 6
- I4 + 2x5 - 2z6.
I4
I5
I6
-3z1 – 312 + 2x3
-1
-2x2 - 14 + 215 – 316
-1
-I3 + I3 - 2x4 + 2z6.
-I1 + 212 - 3r3 - 2x4 + 25
1
%3D
271 + 2x2 – 213 – 214 + 2x5 + 216
1
2.
2x1 + 12 + I3 – 14 + 215
211 – 3z3 – 3z4 – 215
-I1 + 2z2 + 2a3 + 2x4 + z6
I5
I6
- 16
-1
I6
1.
%3D
-1
| 211 + 12 - 3r3 + 14 - I5 – 16
I6
3.
I4
I5
I3
|-2x1 - 3z3 - 4 - 3z5
I6
I4
I5
I1 - 213 – 314 – 15 + I6
| -371 + 12 – 213 – 314 – 316
I1
5.
I4
I5
-3z1 - 12 - T3 + 214 + 2x6
Iz + 2x3 – I4 – 215
|-211 + 12 - T4 + 2z5 + I6
-3z3 – 214 – Is + 216
6.
I4
I5
I6
|| || || ||
|| ||||
|| ||
4.
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