(a) Find the rank of the following matrix for all values of a 1 -1 2 2-1 a 5 1 10 -61 Show your working. (b) Consider the complex vector space C² (with complex scalars). Find the real number a, if it exists, such that the following two vectors v₁ and V₂ in C² are linearly dependent: V₁ = (1 + i, 3-i), V₂ = (-2-i, a-3i).
(a) Find the rank of the following matrix for all values of a 1 -1 2 2-1 a 5 1 10 -61 Show your working. (b) Consider the complex vector space C² (with complex scalars). Find the real number a, if it exists, such that the following two vectors v₁ and V₂ in C² are linearly dependent: V₁ = (1 + i, 3-i), V₂ = (-2-i, a-3i).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 29E
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