Math Problem Solver

(* Define the spanning vectors *)

v1 = {2, -4, 3, -1};

v2 = {-3, 5, -5, -1};

v3 = {6, -2, 7, 5};

(* Define the basis vectors with unknown x *)

b1 = {1, 2, 0, 1};

b2 = {-3, 2, -3, 0};

x = {x1, x2, x3, x4};

(* Solve for x such that {b1, b2, x} spans the same space as {v1, v2, v3} *)

Solve[

LinearSolve[

Transpose[{v1, v2, v3}], {b1, b2, x}] == IdentityMatrix[3],

{x1, x2, x3, x4}

]