1. Consider the linear system x+y=6 3x - y = 2 (a) Express this linear system as a vector equation x₁ + x₂v = b for appropriately chosen vectors u, v, and b. (b) Express this linear system in matrix form Ax = b for appropriately chosen A, x, and b. (c) Solve this linear system geometrically by sketching out the lines determined by each linear equation. Use the example from lecture as reference. (d) Solve the linear system in terms of linear combinations of vectors in R2. Use the example from lecture as reference.

Q: Let the set {v,, v2} be linearly dependent. Determine whether the set {v, + 4v,, 5v, - v2} is also…

A:

Q: Give the parametric vector form of the general solution of the following system of linear equations:…

A:

Q: Suppose the solution set of a certain system of linear equations can be described as x₁ = 5 + 3x3,…

A: Suppose the solution set of a certain system of linear equations can be described as x1=5+3x3,…

Q: 7. (а) X1 3x2 = 1 2x1 - 6х, — 2 | %3D

A: The solution is given as

Q: 2. Consider the set of vectors in R4 S = {(1, 0,-1, 1), (2, -1, 0, 1), (1, 1, 2, 1)}. (a) Determine…

A:

Q: 2. Rearrange the equations to form a strictly diagonally dominant system. Apply two steps of the…

A: The complete solutions are given below

Q: O =) write a system of the given vector equation 4 X2 а) 4х, + 4х2 = 3 -4x1 = -3 9x1-7x 2 = 1 4 x₁ +…

A: To write the given system equations.

Q: Suppose the solution set of a certain system of linear equations can be described as ×₁ = 6+5x3, x2…

A: Step 1: Step 2: Thank you.  Step 3: Step 4:

Q: X₁ Describe the solution set, x = x₂ X3 fill in the answer boxes within your choice. (Type an…

A:

Q: Use carmer's rule to solve the system  x+2y-4z = 0 2x+5y      = 4         y- z   = 3

A: Firstly find ∆,∆x,∆y  and ∆z .If ∆,∆x,∆y,∆z≠0 then system has unique solution.and solution is…

Q: Solve the system of equations by Cramer's rule: 4x +3y = 2 11x + y+2z = 3 x+5y+2z =1

A: