A basis

E

for the nullspace of

A=([-3,3,-4,5],[-12,12,-12,24])

has the form

{(x,1,y,0),(z,0,t,1)}

.\ (L.O.1) Determine

x,y,z,t

.\ (A)

x=1,y=0,z=-2,t=-1

\ (B)

x=-2,y=-1,z=1,t=5

\ (C) Other answers are\ wrong.\ (D)

x=-2,y=-1,z=0,t=1

\ (E)

x=-2,y=0,z=-2,t=-5

\ (L.O.1) Find

u

and

v

such that

w=(u,2,v,5)

is in

\\\\Nu ll(A)

. (A)

u=-7.5,v=-8

\ (B)

u=-7,v

\

=-4.5

\ (C)

u=-12,v=-1.5

\ (D) Other answer are wrong.\ (E)

u=-8,v=-5

\ (L.O.1) Let

\\\\theta

be a vector in

\\\\Nu ll(A)

such that

[\\\\theta ]_(E)=(5,5)^(T)

. Find the vector

\\\\theta

.\ (A)

(75,75,80,145)

\ (B)

(-75,75,-80,145)

\ (C) Other answer are wrong.\ (D)

(5,5,5,5)

\ (E)

(-5,5,-5,5)

\ (L.O.1) Let

F

be another basis of

\\\\Nu ll(A)

and the transition matrix from

F

to

E

is

T_(F->E)=

\

[[f_(1)]_(E)[f_(2)]_(E)]=([1,-4],[5,-19])

. Find the coordinate vector of

\\\\theta

with respect to

F

.\ (A) Other answer are wrong.\ (B)

(-74.5,-20.5)^(T)

.\ (C)

(-14.5,-70.5)^(T)

.\ (D)

(-75,-20)^(T)

.\ (E)

(-15,-70)^(T)

.

A basis E for the nullspace of A=(312312412524) has the form {(x,1,y,0),(z,0,t,1)}. 4. (L.O.1) Determine x,y,z,t. (A)x=1,y=0,z=2,t=1(B)x=2,y=1,z=1,t=5(C)Otheranswersare wrong. (D) x=2,y=1,z=0,t=1 (E) x=2,y=0,z=2,t=5 5. (L.O.1) Find u and v such that w=(u,2,v,5) is in Null(A). (A) u=7.5,v=8 =4.5 (C) u=12,v=1.5 (D) Other answer are wrong. (E) u=8,v=5 (B) u=7,v 6. (L.O.1) Let be a vector in Null(A) such that []E=(5,5)T. Find the vector . (A) (75,75,80,145) (B) (75,75,80,145) (C) Other answer are wrong. (D) (5,5,5,5) (E) (5,5,5,5) 7. (L.O.1) Let F be another basis of Null(A) and the transition matrix from F to E is TFE= [[f1]E[f2]E]=(15419). Find the coordinate vector of with respect to F. (A) Other answer are wrong. (B) (74.5,20.5)T. (C) (14.5,70.5)T. (D) (75,20)T. (E) (15,70)T