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1. For the matrix A = -1 - 1.1 a. AT b. det A c. A-1 -1 0 2 -1 find the, 2 0 -1

1. For the matrix A = -1 - 1.1 a. AT b. det A c. A-1 -1 0 2 -1 find the, 2 0 -1

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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1. 2. 3. For the matrix A=-1 -=& a. AT b. det A c. A-1 1 -1 2 0 -1 Prove that for any two invertible square matrices A and B (AB)-¹ = B-¹A-¹ (Hint: start from (AB)(AB)−¹ = I ) b. The differential 0 44 -1 find the, 2 (d₁) [k11 K12 K13] If d=d₂and K = |k21 k22 K23, where K is symmetric, write K31 K32 K33¹ (d3) a. The scalar quadratic form U = dTK d_explicitly au əd ||| au ad₁ au in terms of d and K ad₂ au მძვ (Hint: Remember that K is symmetric)
Transcribed Image Text:1. 2. 3. For the matrix A=-1 -=& a. AT b. det A c. A-1 1 -1 2 0 -1 Prove that for any two invertible square matrices A and B (AB)-¹ = B-¹A-¹ (Hint: start from (AB)(AB)−¹ = I ) b. The differential 0 44 -1 find the, 2 (d₁) [k11 K12 K13] If d=d₂and K = |k21 k22 K23, where K is symmetric, write K31 K32 K33¹ (d3) a. The scalar quadratic form U = dTK d_explicitly au əd ||| au ad₁ au in terms of d and K ad₂ au მძვ (Hint: Remember that K is symmetric)
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