A square matrix A is called half-magic if the sum of the numbers in each row and column is the same. The common sum in each row and column is denoted by s(A) and is called the magic sum of the matrix A. Let V be the vector space of 2 x 2 half-magic squares. (a) Find Consider the linear operator L : V → V that subtracts the magic sum from every entry in the matrix. More preciselly, L(A) := A – s(A) (b) Find L( 3 (c) Find an ordered basis B for V. B= ( (d) Find the matrix [L] of L in your chosen basis B. [L] =
A square matrix A is called half-magic if the sum of the numbers in each row and column is the same. The common sum in each row and column is denoted by s(A) and is called the magic sum of the matrix A. Let V be the vector space of 2 x 2 half-magic squares. (a) Find Consider the linear operator L : V → V that subtracts the magic sum from every entry in the matrix. More preciselly, L(A) := A – s(A) (b) Find L( 3 (c) Find an ordered basis B for V. B= ( (d) Find the matrix [L] of L in your chosen basis B. [L] =
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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![A square matrix A is called half-magic if the sum of the numbers in each row and column is the same. The common sum in each row and column is
denoted by s(A) and is called the magic sum of the matrix A. Let V be the vector space of 2 x 2 half-magic squares.
(a) Find
Consider the linear operator L : V → V that subtracts the magic sum from every entry in the matrix. More preciselly, L(A) := A – s(A)
(b) Find
L(
3
(c) Find an ordered basis B for V.
B= (
(d) Find the matrix [L] of L in your chosen basis B.
[L] =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf9afb00-fe7a-4f66-82c7-41c2656d6087%2Fa3c03bc8-529f-41d0-ace5-366b4a55f82a%2F9pru4d_processed.png&w=3840&q=75)
Transcribed Image Text:A square matrix A is called half-magic if the sum of the numbers in each row and column is the same. The common sum in each row and column is
denoted by s(A) and is called the magic sum of the matrix A. Let V be the vector space of 2 x 2 half-magic squares.
(a) Find
Consider the linear operator L : V → V that subtracts the magic sum from every entry in the matrix. More preciselly, L(A) := A – s(A)
(b) Find
L(
3
(c) Find an ordered basis B for V.
B= (
(d) Find the matrix [L] of L in your chosen basis B.
[L] =
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