# Direct Sum of two Subspaces

• April 15th 2010, 10:19 AM
charikaar
Direct Sum of two Subspaces
let U be subspace of $R^4$ spanned by the vectors
$u_1=(1,-2,5,-3),u_2=(2,3,1,-4),u_3=(3,8,-3,-5)$

the vectors $v_1=(1,-2,5,-3),v_2(0,7,-9,2)$ form basis for the Subspace U. and $v_1,v_2,v_3=(0,0,1,0),v_4=(0,0,0,1)$ form basis for $R^4$. How do i find the subspace W of $R^4$ such that $R^4=U \oplus W$

Thanks for any help.
• April 15th 2010, 12:01 PM
Drexel28
Quote:

Originally Posted by charikaar
let U be subspace of $R^4$ spanned by the vectors
$u_1=(1,-2,5,-3),u_2=(2,3,1,-4),u_3=(3,8,-3,-5)$

the vectors $v_1=(1,-2,5,-3),v_2(0,7,-9,2)$ form basis for the Subspace U. and $v_1,v_2,v_3=(0,0,1,0),v_4=(0,0,0,1)$ form basis for $R^4$. How do i find the subspace W of $R^4$ such that $R^4=U \oplus W$

Thanks for any help.

Hint: think orthogonal complement.
• April 16th 2010, 01:18 AM
charikaar