7. Consider an n x n matrix A that is not a null matrix. Suppose that A is idempotent, and define matrix B by B = I −k²A, where k € R is a parameter. Which of the options below is the set of ALL values k such that B is idempotent? a) R b) {0} {0,1} d) {-1,0} e) {-1,0, 1} f) {-3,0,3} g) The set of all positive whole numbers. h) None of the above.

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter2: Mathematics For Microeconomics
Section: Chapter Questions
Problem 2.6P
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7. Consider an n x n matrix A that is not a null matrix. Suppose that A is idempotent,
and define matrix B by B = I −k²A, where ke R is a parameter. Which of the options
below is the set of ALL values k such that B is idempotent?
a) R
b) {0}
{0, 1}
d) {-1,0}
e) {-1,0, 1}
f) {-3,0,3}
g) The set of all positive whole numbers.
h) None of the above.
Transcribed Image Text:7. Consider an n x n matrix A that is not a null matrix. Suppose that A is idempotent, and define matrix B by B = I −k²A, where ke R is a parameter. Which of the options below is the set of ALL values k such that B is idempotent? a) R b) {0} {0, 1} d) {-1,0} e) {-1,0, 1} f) {-3,0,3} g) The set of all positive whole numbers. h) None of the above.
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