Let V = M² X 2 (R) be the vector space of all real 2 x 2 matrices. Determine if the following matrices are linearly independent; if linearly dependent, find a nontrivial linear combination of the form a₁A₁ + a₂A₂ + ªa343 +444 that results in the zero matrix. (Give ₁, 2, 3, and 4 as real numbers. If the matrices are linearly independent, enter INDEPENDENT.) A₁ = · -[ : :], ^₂ -[ : 8 ]· ^, -[: 0], A₂ (a₁a₂₁ 3₁₁) = 4-[48] and A₁ =
Let V = M² X 2 (R) be the vector space of all real 2 x 2 matrices. Determine if the following matrices are linearly independent; if linearly dependent, find a nontrivial linear combination of the form a₁A₁ + a₂A₂ + ªa343 +444 that results in the zero matrix. (Give ₁, 2, 3, and 4 as real numbers. If the matrices are linearly independent, enter INDEPENDENT.) A₁ = · -[ : :], ^₂ -[ : 8 ]· ^, -[: 0], A₂ (a₁a₂₁ 3₁₁) = 4-[48] and A₁ =
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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