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a) If 42₁]=²2x1+²[*] x, then x = 3, y = 2, and z = Z y = 1. 5

a) If 42₁]=²2x1+²[*] x, then x = 3, y = 2, and z = Z y = 1. 5

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.6: Matrices
Problem 4E: Let A=[aij]23 where aij=i+j, and let B=[bij]34 where bij=2ij. If AB=[cij]24, write a formula for cij...
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Answer each of the following as True or False justifying your answers [x y a) If 4 ₁] = 2 [2x 1 + ² [²/ 21] 2, and z = 1. [4 X = _*], then x = 3, y = b) If v₁ (1,2), v₂ = (3,4), v3 = (−1,0), then u = (6,8) is a linear combination of v₁, V2, and v3 where u = 20₁ 20₂- V3. c) If A² = A, Then I - 2A = (1 - 2A)-¹. - d) If A is n x n skew-symmetric matrix where n is an odd integer number, then A is singular. e) If A = [¹³₂], Then A is singular only if k = 4. k2, k = 1 3 2
Transcribed Image Text:Answer each of the following as True or False justifying your answers [x y a) If 4 ₁] = 2 [2x 1 + ² [²/ 21] 2, and z = 1. [4 X = _*], then x = 3, y = b) If v₁ (1,2), v₂ = (3,4), v3 = (−1,0), then u = (6,8) is a linear combination of v₁, V2, and v3 where u = 20₁ 20₂- V3. c) If A² = A, Then I - 2A = (1 - 2A)-¹. - d) If A is n x n skew-symmetric matrix where n is an odd integer number, then A is singular. e) If A = [¹³₂], Then A is singular only if k = 4. k2, k = 1 3 2
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