All subsets of the set s = {(i, 0), (0, i), (i, i)} that form a basis for r2 is
{( 0,1) (-1,1)}
{(1,0)(0,1)}
{(1,0)(-1,1)}
A fixed A is a subset of some other set B if all elements of set A are factors of set B. In other phrases, set A is contained within set B. The subset relationship is denoted as A⊂B.
Subsets are a part of one of the mathematical ideas known assets. a hard and fast is a set of items or factors, grouped within the curly braces, consisting of {a,b,c,d}. If a set A is a set of even numbers and set B includes {2, 4,6}, then B is stated to be a subset of A, denoted by B⊆A and A is the superset of B.
In mathematics, set A is a subset of a fixed B if all factors of A are also elements of B; B is then a superset of A. It's far possible for A and B to be equal; if they may be unequal, then A is a proper subset of B. The relationship of one set being a subset of every other is known as inclusion.
A set which is (is linearly independent andoil generates/ spans the space (like R) is called a baris.
S= (1,0), (0,1), (-1))}
option-1
As, dimension of R²=2, so, Ary set
conists of three vectors cannot be baris for R²
so, option-1 is wrong.
option-2
As, dimention of R2-2.
{(10), (-11)} is a linearly independent
subset of S. so And as, this subset
has 2 vectors so it will as also
span R se, it will be a baris
of IR?
So, option-6 is correct
{(0,1)} is linearly independent subset
option-7
As (LO) has one vector. So, it cannot
Span/generate R so, it also cannot be balis
for R2
of S.
But it cannot span R²
So ut cannot
be a baris of R2
se, option-2 is wrong.
Option-3
AS, {(0,1), (-1,1)} is linearly independent
So, option -7, is wrong.
Answer
[as fox amy KER, (-1,1) K (0,1)] subset of s
And also as dim {(0,1), (-11)}=2
which is same as the dimention of IR2
so {(0,1), (-11)} forms a baris of R2
{(1,0), (0,1), (-11)}
{(1,0)}
So, option-3 is
Connect
option-4
{(1,0), (3, 1)} is standard balis of R2
which is subset of S.
10
[{(1,0), (0,1)}]
So, option-4 is correct.
option-5
{(-11)}
consists of one vertex,
so, ut cannot span R², so, ut cannot
be a baris of R²
9090
LO {(1,0), (-1,1)}]
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