Linear Algebra question 49. Verify that det A = det B + det C, whereall a12U₁ + v₁a21a22U₂+U₂a32Uz + V3A ==a31a11a12a12U₁a22922U2= a21a31a 32a32 UzNote, however, that A is not the same as B + C.B =alla21a31--- [V1U2V3

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49. Verify that det A = det B + det C, where all a12 U₁ + v₁ a21 a22 U₂+U₂ a31 a32 Uz + V3 A = all a12 V1 U₁ all a21 a22 V2 a21 922 U12 a31 a32 V3 a31 a32 Uz Note, however, that A is not the same as B + C. B = a12

49. Verify that det A = det B + det C, where all a12 U₁ + v₁ a21 a22 U₂+U₂ a31 a32 Uz + V3 A = all a12 V1 U₁ all a21 a22 V2 a21 922 U12 a31 a32 V3 a31 a32 Uz Note, however, that A is not the same as B + C. B = a12

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.7: Introduction To Coding Theory (optional)

Problem 13E

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Linear Algebra question

49. Verify that det A = det B + det C, where
all a12
U₁ + v₁
a21
a22
U₂+U₂
a32
Uz + V3
A =
=
a31
a11
a12
a12
U₁
a22
922
U2
= a21
a31
a 32
a32 Uz
Note, however, that A is not the same as B + C.
B =
all
a21
a31
--- [
V1
U2
V3

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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