Question

Let WW be a subset of a vector space VV. By justifying your answer, determine whether WW is a subspace of VV.

(a) [5 marks] W={(x1,x2,x3,x4):x1x4=0}W={(x1,x2,x3,x4):x1x4=0} and V=R4V=R4.

(b) [5 marks] W={A:|A|≥1}W={A:|A|≥1} and V=M3,3V=M3,3, where |A||A| is the determinant of AA.

(c) [10 marks] W={p(x)=a0+a1x+a2x2+a3x3:a0=a1anda2=a3}W={p(x)=a0+a1x+a2x2+a3x3:a0=a1anda2=a3} and V=P3V=P3.

Answer #1

please upvote

Determine whether the given set ?S is a subspace of the vector
space ?V.
A. ?=?2V=P2, and ?S is the subset of ?2P2
consisting of all polynomials of the form
?(?)=?2+?.p(x)=x2+c.
B. ?=?5(?)V=C5(I), and ?S is the subset of ?V
consisting of those functions satisfying the differential equation
?(5)=0.y(5)=0.
C. ?V is the vector space of all real-valued
functions defined on the interval [?,?][a,b], and ?S is the subset
of ?V consisting of those functions satisfying
?(?)=?(?).f(a)=f(b).
D. ?=?3(?)V=C3(I), and...

Determine if the given set V is a subspace of the vector space
W, where
a) V={polynomials of degree at most n with p(0)=0} and W=
{polynomials of degree at most n}
b) V={all diagonal n x n matrices with real entries} and W=all n
x n matrices with real entries
*Can you please show each step and little bit of an explanation
on how you got the answer, struggling to learn this concept?*

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