Linear Algebra Answers

solve the following linear programming problem using graphical methods
Minimize z= 2x+8y
Subject to x-y > -7
3x+2y > 24
x > 0
y > 0
find the minimum z value and name the points

A linear tansformation
T:U→F
is a called a ………………… if
T(α1u1+α2u2)=α1T(u1)+α2T(u2)
, for
α1,α2∈F
and
u1,u2∈U
.
linear dimensional
linear function
linear functional
linear dimension

Let U and V be vector spaces over a field F and dim U = n. Let
T:U→V
be a linear operator, then rank (T) + nullity (T) = ……
0
1
n-1
n

Let U and V be vector spaces over a field F.A linear transformation
T:U→V
that is onto is called …………..
invertible
surjective
injective
singular

A linear tansformation is invertible if
reversible
onto
one-one and onto
one-one

Let
T:U→V
be a linear transformation, where U and V are of the same finite dimension. Then the following but one statements are equivalent
T is a homomorphism
T is an isomorphism
T is 1 - 1
T is onto

Let U be a vector space over a field F,a function T(u) = u for all
u∈U
is called ……………..
linear transformation
identity transformation
non linear transformation
reflective transformation

Let U and V be vector spaces over a field F,a function
T:U→V
such that
T(u1+u2)=T(u1)+T(u2)
, for
u1,u2∈U
and
T(αu)=αT(u)
for
α∈F
and
u∈U
is called a ………….
vector space
transformation
linear transformation
nullity

Let U and V be vector spaces over a field F. Let
T:U→V
be a linear transformation, then the set
[T(x)]x∈U
is called the
transformation
space
kernel of T
range of T

1 Let V be a vector space over a field F and function
I:V→V
be the identity transformation. Find range of I R(I)
{0}
{1}
{0,1}
none of the above