Suppose that A is a 6 × 7 matrix, with rank 5. (1) For the equation Ax = b, x exists in R^n, ⃗b ∈ R^m to make sense, what must n equal? What must m equal? (2) Is the equation Ax = b consistent for every b in R^m (for the value of m found in part 1)? Why or why not? (3) When the equation Ax = b is consistent, how many free variables will the solution have?

Suppose that A is a 6 × 7 matrix, with rank 5. (1) For the equation Ax = b, x exists in R^n, ⃗b ∈ R^m to make sense, what must n equal? What must m equal? (2) Is the equation Ax = b consistent for every b in R^m (for the value of m found in part 1)? Why or why not? (3) When the equation Ax = b is consistent, how many free variables will the solution have?

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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