6. Suppose an n x n matrix A satisfies the equation A22A+l=0. Show that A3 = 3A-2l and A4=4A 3| 7. Let A be the following Matrix: u328] 4- Compute the matrices A2, AN and A'l. I Find the numbers p and q such that A2=pA+qL where l is the 2x2 identity matrix. a Let B=A-tl, where t is a scalar. For which value oft is B not invertible? 8. Determine if b is a linear combination ofthe vectors a1, a2 and a3 where 31:\" '_ 10]:32=[ 2 ' 1 1],a3= [3 1 3]b= [s 4 7] If b is a linear combination of the vectors a], a2 and a3, express b as linear combination of the vectors a1, a1 and a3. 9. Normalize the following vectors: a) u = (3,4) b) v = (4, -2, -3, 8) c) w: (1/2, 2/3, 4/4) 10. Determine whether the given matrix is singular or nonsingular. If it is nonsingular, find its inverse a. [60 3 2] b. [1230 42 151] c. [423210 1 20]