Linear Algebra is the topic 11000-1 1000 0 001 0 0001 0000 1000 0(E1):col2col2+col₁(E2):col3 cols-col₁Bker (8¹)101 10 10 00 000---6V20Exercise Check that V2, V3, V4, V5 € ker(8¹) by the definition of kernel.V3The key is now that the vectors of Q under the zero "columns" of 8¹. Q will actually form a basis for ker(8¹). So if we callv₁ through v5 the five columns of 8¹ - Q, the four vectors in our case that form a basis for the kernel are:0-100 01000 1 00 0 1V400001V58¹. QQ = IE₂ E₁)0

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Answered: 1 1 0 0 0 -1 100 0 0 00 1 0 00 0 1 00 0…

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 is the topic

1
1
0
0
0
-1 100
0 0 00
1 0 00
0
1 00
0
0 10
0
0 0
(E1):col2col2+col₁
(E2):col3 cols-col₁
Bker (8¹)
1
0
1 1
0 1
0 0
0 0
00
---6
V2
0
Exercise Check that V2, V3, V4, V5 € ker(8¹) by the definition of kernel.
V3
The key is now that the vectors of Q under the zero "columns" of 8¹. Q will actually form a basis for ker(8¹). So if we call
v₁ through v5 the five columns of 8¹ - Q, the four vectors in our case that form a basis for the kernel are:
0
-1
0
0 0
1
0
0
0 1 0
0 0 1
V4
00
00
1
V5
8¹. Q
Q = IE₂ E₁)
0

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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