Answered: For the matrix A = 1 4 7 258 3 69 find…

For the matrix A = 1 4 7 258 3 69 find the elimination matrix L₁(A), compute the product L₁(A)A by matrix multiplication, and compute the same product L₁(A)A by using Lemma 2.31.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.3: The Inverse Of A Matrix

Problem 79E: Let A,D, and P be nn matrices satisfying AP=PD. Assume that P is nonsingular and solve this for A....

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Question

Using the Lemma pictured, need help with this question. Thank you :)

For the matrix
A =
1 4 7
258
3 69
find the elimination matrix L₁(A), compute the product L₁(A)A by
matrix multiplication, and compute the same product L₁(A)A by using
Lemma 2.31.

Lemma 2.31: action of elimination matrices
Let A € Rdxd be a matrix and let k € {1,...,d – 1} with Ak,k ‡ 0. Then
(Lk (A)A)ij =
Aij,
0,
Aij
i € {1,...,k},
i € {k+1,...,d}, j = k,
Ask Akj, i {k+1,...,d}, j‡k.
Akk

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