Problem (i) Consider the normalized vector v in R³ and the permutation matrix P, respectively () 0 1 0 P = |0 0 1 1 0 0 1 V3 -1 Are the three vectors v, Pv, P²v linearly independent? (ii) Consider the 4 x 4 symmetric matrix A and the vector b in R' 0 1 0 0 1 0 1 0 0 1 0 1 \0 0 1 0, A = b = Are the vectors b, Ab, A²b, A³b in Rª linearly independent? Show that the matrix A is invertible. Look at the column vectors of the matrix A 0000 Find the inverse of A.

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