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(Describe the steps of the proof carefully so that the Problem 5. Short Proof logic you follow is clear.) Let a, and a₂ be two linearly independent vectors in R5. Prove that the 3 x 5 matrix B a B = a +a₁a Laza+al. cannot have rank greater than 2 for any values of a1, 02 € R.

(Describe the steps of the proof carefully so that the Problem 5. Short Proof logic you follow is clear.) Let a, and a₂ be two linearly independent vectors in R5. Prove that the 3 x 5 matrix B a B = a +a₁a Laza+al. cannot have rank greater than 2 for any values of a1, 02 € R.

Advanced Engineering Mathematics
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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Can The solver please include hand written steps and all matrix notation possible? Thank you! 

  

។ (Describe the steps of the proof carefully so that the Problem 5. Short Proof logic you follow is clear.) Let a₁ and a2 be two linearly independent vectors in R5. Prove that the 3 x 5 matrix B T a B = a +a₁a Laza + a cannot have rank greater than 2 for any values of a₁,02 € R.
Transcribed Image Text:។ (Describe the steps of the proof carefully so that the Problem 5. Short Proof logic you follow is clear.) Let a₁ and a2 be two linearly independent vectors in R5. Prove that the 3 x 5 matrix B T a B = a +a₁a Laza + a cannot have rank greater than 2 for any values of a₁,02 € R.
Expert Solution
Step 1

It is given that, a1 and a2 be two linearly independent vectors in ℝ5.

And, B be the 3×5 matrix given by ;     B = a1Ta2T + α1a1Tα2a2T + a1T

Then, we have to show that, the matrix B cannot have rank greater than 2 for any values α1, α2 ∈ ℝ.

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