5. Let x = [2,1,0],x = [1,2,1], v = [a,b,c]T (10+10+15 pts) a) Find a condition...

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5. Let x₁ = [2,1,0],x₁ = [1,2,1]", v = [a,b,c]T (10+10+15 pts) a) Find a condition that a, b, c must satisfy for the set of vectors {x₁, x2, v} to be linearly dependent. b) Find a vector x3 such that {x₁, x2, x3} is a linearly independent set of vectors. Find the determinant and the rank of the 3-by-3 matrix composed of columns X₁, X2, X3. c) Solve the following linear system of equations: 2x + y = 1 x + 2y + z = 2 (x -y + 2z = 1 5. Let x₁ = [2,1,0],x₁ = [1,2,1]", v = [a,b,c]T (10+10+15 pts) a) Find a condition that a, b, c must satisfy for the set of vectors {x₁, x2, v} to be linearly dependent. b) Find a vector x3 such that {x₁, x2, x3} is a linearly independent set of vectors. Find the determinant and the rank of the 3-by-3 matrix composed of columns X₁, X2, X3. c) Solve the following linear system of equations: 2x + y = 1 x + 2y + z = 2 (x -y + 2z = 1