Question 2. Define

\\\\Phi :R^(2\\\\times 2)->P_(2)

by\

\\\\Phi ([[a,b],[c,d]])=(a+b)+(2d)x+bx^(2).

\ Let\

B={[[1,0],[0,0]],[[0,1],[0,0]],[[0,0],[1,0]],[[0,0],[0,1]]} and \\\\gamma ={1,x,x^(2)}

\ (a) Compute

[\\\\Phi ]_(B)^(\\\\gamma )

.\ (b) Determine

rk([\\\\Phi ]_(B)^(\\\\gamma ))

.\ (c) Compute the kernel and image of

\\\\Phi

. What are nullity

(\\\\Phi )

and range

(\\\\Phi )

?

Question 2. Define :R22P2 by ([acbd])=(a+b)+(2d)x+bx2. Let B={[1000],[0010],[0100],[0001]}and={1,x,x2} (a) Compute []B. (b) Determine rk([]B). (c) Compute the kernel and image of . What are nullity () and range ()