Question

Find a basis for the following subspace of

R

5

.

J

=

{

⃗

x

∈

R

5

∣

x

1

=

x

2

=

x

5

,

x

3

+

x

4

=

}

What is the dimension of

J

?

Answer 1

$J=\{x∈R^5∣x_1=x_2=x_5,x_3+x_4=0\}$

any vector in subspace:

$V=(x_1,x_1,x_3,-x_3,x_1)=x_1(1,1,0,0,1)+x_3(0,0,1,-1,0)$

basis:

$(1,1,0,0,1),(0,0,1,-1,0)$

there are 2 vectors in basis, so dimension of subspace is 2