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

See similar textbooks

Similar questions

Using only these numbers ( 2,1,9 ) as coefficients, create a matrix of size 5x5 (with all coefficients non-zero) that has rank 3. a) Explain why the rank is equal to 3.
Q6 Needed to be solved correctly in 20 minutes in the order to get positive feedback please provide me hundred percent correct answer in the order to get positive feedback Hundred percent efficiency needed please
Q3/create a matrix A and 1- add fourth & fifth rows equal to [1 2 3] by using [1 2 31 A= 4 5 6 [7 8 9 9] OA([4,5],:)-[1 2 3;1 2 3] O a([4,5],:)= [1 2 3;1 2 3] O A((4,5),:) [1 2 3;1 2 3] O a(,[4,5])=[1 2 3;1 2 3]
A is a 2x2 matrix. Row 1 is: 7/3 -2/3 Row 2 is: 2/3 2/3 Please answer 1 and 2. To clarify, Question 2 is: Compute A^(112)
For the equation ax^2 + bxy + cy^2 = 0, let A = [a b/2 b/2 c] (A is a 2x2 matrix) Show that if det(A) = 0, then the graph of ax^2 + bxy + cy^2 = 0 is a line. Show that if det(A) != 0, then the graph of ax^2 + bxy + cy^2 = 0 is two intersecting lines.
G1/ Find A' of the matrix 3 -1 A = %3D 2. -4
Show that if A is square matrix that satisfies the equation 2 A² - A - I = O, then its inverse is A-¹ = 2 A-I. The equation 24² - A - I = O implies that ---Select--- ✓. It follows that ---Select--- ✓. Notice the last equation means that ---Select--- multiplied with A is the identity, which is what we wanted to prove.
Please don't provide hand written solution
Please answer with explanation. I will really upvote
Pls solve this question correctly instantly in 5 min i will give u 3 like for sure
Solve the matrix equation AX = B for X. 12 ^-]-[] B = 6 7 A = X || 18 14 59
14. Determine elementary matrices E₁, E2, ..., Ek that reduce 2 A ^= [² -1 ] 1 3 to reduced row-echelon form. Verify by direct multi- plication that E₁ E2... EkA = 1₂.