please help me with this linear algebra question Given the determinants of the following matrices:2 -4 2-62 -4 -12 −63 -66-63-6 9 -61 -2 14 21 -2 1 2-2 5 -1 7-2 5 197Find the (unique) solution to the following system:det2x1−4x2+2x3−6x43x1-6x2+6x3-6x4 = 9x1-2x2+x3+2x414-2x1+5x2-x3+7x419X=00===:30,-12det= 150, det2-12391141-2 19 -1 72 -66-6227-60, det23-6 6-2 11-2 5 -1-4 2-1291419= 120, det-6-12 -4 2-6 6-6-2 1 29141951 727=-90

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Answered: Given the determinants of the following…

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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please help me with this linear algebra question

Given the determinants of the following matrices:
2 -4 2-6
2 -4 -12 −6
3 -6
6-6
3-6 9 -6
1 -2 14 2
1 -2 1 2
-2 5 -1 7
-2 5 19
7
Find the (unique) solution to the following system:
det
2x1−4x2+2x3−6x4
3x1-6x2+6x3-6x4 = 9
x1-2x2+x3+2x4
14
-2x1+5x2-x3+7x4
19
X=
0
0
=
=
=
:30,
-12
det
= 150, det
2
-12
3
9
1
14
1
-2 19 -1 7
2 -6
6-6
2
27
-60, det
2
3
-6 6
-2 1
1
-2 5 -1
-4 2-12
9
14
19
= 120, det
-6
-12 -4 2
-6 6-6
-2 1 2
9
14
19
5
1 7
27
=-90

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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