to be consistent? 1302 DA X₁ + 5x₂ = b5 Working with Proofs 39. Prove: If k0, then A and kA have the same rank. 40. Prove: If a matrix A is not square, then either the row vectors or the column vectors of A are linearly dependent. 41. Use Theorem 4.9.3 to prove Theorem 4.9.4. 42. Prove Theorem 4.9.7(b). 43. Prove: If a vector v in R" is orthogonal to each vector in a basis for a subspace W of R", then v is orthogonal to every vector in W.

to be consistent? 1302 DA X₁ + 5x₂ = b5 Working with Proofs 39. Prove: If k0, then A and kA have the same rank. 40. Prove: If a matrix A is not square, then either the row vectors or the column vectors of A are linearly dependent. 41. Use Theorem 4.9.3 to prove Theorem 4.9.4. 42. Prove Theorem 4.9.7(b). 43. Prove: If a vector v in R" is orthogonal to each vector in a basis for a subspace W of R", then v is orthogonal to every vector in W.

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 30E

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