If T is defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is unique. Let 1 -7 -25 -4 A= [3] -3 12 39 and b = Find a single vector x whose image under T is b. 3 -1 x= 1 0 Is the vector x found in the previous step unique? O A. No, because there are no free variables in the system of equations. O B. No, because there is a free variable in the system of equations. O C. Yes, because there is a free variable in the system of equations. O D. Yes, because there are no free variables in the system of equations.

Assume that n(U)=90n(U)=90, n(A)=41n(A)=41, n(B′)=50n(B′)=50, and n(A∪B)=63n(A∪B)=63. Find n(A∩B)

Spent a lot of time solving it, need some help

Determine whether b can be written as a linear combination of a₁, a2, and a3. In other words, determine whether weights X₁, X₂, and X3 exist, such that x, a₁ +X₂ª₂ +X3ª3 = b. Determine the weights X₁, X₂, and x3 if possible. ·0-0-0 2 a₂ 4 1 Let a₁ = 1 -3 O A. x₁ = 2, X₂ = 1, X3 = 2 O B. x₁=1, x₂ = 0, X3 = 1 OC. x₁ = -2, x2 = -1, x3 = -5 O D. There is no solution. 2 6 and b= 3 -5 -4