9. (2 pts each) Write answer for each of the followings. (Intermediate steps are
ID: 3148636 • Letter: 9
Question
9. (2 pts each) Write answer for each of the followings. (Intermediate steps are NOT necessary) il ard B-1 = 1 [2 3 (i) If A-1 = find the inverse of BA. 2 3 Answer: (ii) If denotes angle between vectors u = (2,3,-5) and v-(-5,2,3), find cos . Answer: (iii) Find a vector u with length v and perpendicular to the plane z += 0 in R. Answer: (iv) Let f(x)-xTAx = z1 + z3 + z{, x E R4, Find A and trace(A). Answer: A= trace(A)-- . (v) If any, which ones of the following matrices are NOT diagonalizable? (Choose all that apply.) 1 10 1 1 0 001 0 0 1 Answer: 12Explanation / Answer
a)
inv(BA) = inv(A) * inv(B)
inv(A) = [1 1 ; 2 3];
inv(B) = [2 3 ; 1 1];
hence
inv(BA) =
ans =
3 4
7 9
ii)
cos t = u*v/(||u||* ||v||)
u.v = (-10 +6 -15) = -19
||u||= sqrt(4+9+25)
||v|| = sqrt(25+4+9)
hence
cos t = -19/38 = -1/2
iii)
normal of plane is (1 1 1)
u = a(1,1,1)
length (u) = sqrt(3)
length ((1,1,1)) = sqrt(3)
hence a = 1
u = (1 1 1)
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