In the name of ALLAH, the most beneficient, the most merciful

Linear Algebra (MTH501)

Question (select most suitable option)

  If \(v_1 = (2, 2, 2), v_2 = (0, 0, 3) \) and \(v_3 = (0, 1, 1) \) span \( R^3 \), then which of the following is true for any arbitrary \(b^r = (b_1, b_2, b_3) \in R^3 \) ?
\( (0, 1, 1) = k_1 (b_1, b_2, b_3) + k_2 (2, 2, 2) + k_3 (0, 0, 3) \)
\( (b_1, b_2, b_3) = k_1 (2, 2, 2) + k_2 (0, 0, 3) + k_3 (0, 1, 1) \)
\( (0, 0, 3) = k_1 (2, 2, 2) + k_2 (b_1, b_2, b_3) + k_3 (0, 1, 1) \)
\( (0, 1, 1) = k_1 (2, 2, 2) + k_2 (0, 0, 3) + k_3 (b_1, b_2, b_3) \)