Find the general solution for system of equations with

Question

Problem # 1

Use determinants to find out if the following three vectors are linearly independent. Show your work and justify your answer.

Problem # 2

Consider the following system of linear equations:

2x₁ + 6x₂ + 8x₃ + 4x₄ =14

2x₁+ x₂ -2x₃ -5x₄ = -3

-x₁ -2x₂ + x₃ + 4x₄ = 9

(a) Find the general solution for this system of equations with respect to the basic matrix B = (^-a₁ ^-a₂ ^-a₄), where ^-a_i represents the i^th, column of A.

(b) Provide the basic solution for the basic matrix defined in part (a).