ignore the lines and solve each question separately please Q Let B (V1, V2, V3, V4] be a basis for R4. Let TRR be the linear transformation such that on the basis vectors V1, V2, V3, V4, its values are: T(v) = 2v1 -2v2 +213 +3v4 T(v2)= = 6v1 +3v3 T(v3)= V1 -V2 +V4 T(v4): = V1 +2v2 +V3 -2v4 (a) Find the matrix for with respect to the basis B: [T] B =? (b) Let x = c1v1 + C2V2 + C3V3 +C4V4, where C1, C2, C3, C4 R. What is [x] = 3(x)=? What is [T(x)]B= = CB(T(x)) =? -3 3 (c) Find the solution of the equation I(x)=h, where b 0 1 (d) Suppose that the vectors v Vare given as follows: 2 V2 22 -2 0 1 H 2 i. Find the change-of-basis matrix P from the standard basis to the basis B. ii. Find the standard matrix stand for the linear transformation T using the Change-of-Basis For- mula and the matrix [T] you have found in part (a). Hint: The change-of-basis matrix P is the 4x4 matrix with columns V1, V2, V3, V4 and [T]stand P[T]BP-1. In order to find the inverse of P, you can search the properties of the matrices whose column vectors. are orthonormal vectors. (e) Compute the trace of the linear operator_I (f) Compute the kernel of the linear operator T w.r.t. basis B