Linear algebra, (D)EProve Propertythe flig statementsproperty li4A) Assume that A and B are in VB) Then, SinceoneAnsis true by reorderingto form a proof.shouldA₁ B₁ V = Max the sum AB is in V = M₂ x +a real numberWe then know that AB is a 3x3 matrix of real numbersthe definition AB, cij = aij x bijByTot aij, bij, cij be the ith entries of the matricesA, B, and C = AⓇRrespectivelyTherefore, AB must be in Wbe as aletters-ex FEDCBA-aij, bij are real numbers, Cij is also

Given: V=M3×3 and two matrices A,B∈M3×3 .There is some statements also given , (A) Assume that A…

Answered: one Prove Property the flig statements…

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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Question

Linear algebra,

(D)
E
Prove Property
the flig statements
property li
4
A) Assume that A and B are in V
B) Then, Since
one
Ans
is true by reordering
to form a proof.
should
A₁ B₁ V = Max the sum AB is in V = M₂ x +
a real number
We then know that AB is a 3x3 matrix of real numbers
the definition AB, cij = aij x bij
By
Tot aij, bij, cij be the ith entries of the matrices
A, B, and C = AⓇR
respectively
Therefore, AB must be in W
be as a
letters-ex FEDCBA-
aij, bij are real numbers, Cij is also

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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