3. Assume DT(d₁,..., dn) and D-¹ = (C₁, C2,..., Cn) are given. Let vector de Rn and an index1 ≤ k ≤n. Assume d' ck 0. If replace k-th row of D by d, that is,DT = (d₁,..., dk-1, d, dk+1,..., dn),=Let D-¹ = (₁, ..., ên). ThenĈiif i = k.dT CkVerify/prove that D-¹ is indeed the inverse of the matrix D.=Cidick if i ‡k,CkCk

Answered: Image /qna-images/answer/115ddbeb-dc25-4f3e-a7f9-ef57ea9fb6e2.jpg

= 3. Assume DT (d₁,..., dn) and D-1 (C₁, C₂,..., Cn) are given. Let vector de Rn and an index 1 ≤ k ≤n. Assume d ck ‡0. If replace k-th row of D by dº, that is, Ck DT = (d₁,..., dk-1, d, dk+1,..., dn), Let D-¹ = (₁, ..., ên). Then {" Ci - dick if ik, if i = k. -1 Verify/prove that D-¹ is indeed the inverse of the matrix D. drck. Ck Ck

= 3. Assume DT (d₁,..., dn) and D-1 (C₁, C₂,..., Cn) are given. Let vector de Rn and an index 1 ≤ k ≤n. Assume d ck ‡0. If replace k-th row of D by dº, that is, Ck DT = (d₁,..., dk-1, d, dk+1,..., dn), Let D-¹ = (₁, ..., ên). Then {" Ci - dick if ik, if i = k. -1 Verify/prove that D-¹ is indeed the inverse of the matrix D. drck. Ck Ck

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.2: Determinants

Problem 10AEXP

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