a1 Question 1. Let u] = , 12 = bz be any two vectors in R3, C1 C2 I y 2 C11 (a) Consider the matrix A = b1 Cl and define the vector C = C12 whose coor- 02 b2 C2 C13 dinates are the cofactors of the first row. Show that this vector is orthogonal to both 71, 12 Hint: Use that the determinant of a matrix with repeated rows is ( and that determinants can be the computed by adjoints of the first row. (b) Show that if u1, uz are linearly dependent, the vector c defined in (a) is the zero vector. (c) Show that if you replace 71, 12 by another basis 31, 12 of the space they span, the new vector & that we obtain with the process on (a) is a multiple of the vector c obtained from the basis #1, u2. (d) (optional) could you generalize the above to R" instead of R3