Question: (6 marks) Let A = [v1 v2 v3 V4] be a 4 x 4 matrix with column vectors V1, V2, V3, V4. Suppose that det(A)

(6 marks) Let A = [v1 v2 v3 V4] be a 4 x 4 matrix with column vectors V1, V2, V3, V4. Suppose that det(A) = 2022. (a) (3 marks) Find the determinant of the matrix [V1+2V2 V2+2V3 V3+2V4 V4+2V1]- (This is a matrix with column vectors V] + 2V2, V2 + 2V3, V3 + 2V4, V4 + 2V1.) (b) (3 marks) Find the determinant of the matrix [V1+V2+V3 V2+V3+V4 V3+V4+V1 V4+V1+V2]- (This is a matrix with column vectors V] + V2 + V3,V2 + V3 + V4, V3 + V4 + V1,V4 + V1 + V2.) Hint: [V1+2V2 V2+2V3 V3+2V4 V4+2V1]=[V1 V2 V3 V4] OONH ONr'O [Or'00 l'OOM

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