My Math Forum Linear algebra, sum of subspaces
 User Name Remember Me? Password

 Linear Algebra Linear Algebra Math Forum

 December 1st, 2018, 08:05 AM #1 Newbie   Joined: Dec 2018 From: kazakhstan Posts: 1 Thanks: 0 Linear algebra, sum of subspaces Let U1, U2, U3 be subspaces of R^4: U1 = {(a,b,c,d):a=b=c} U2 = {(a,b,c,d):a+b-c+d=0; c-2d=0} U3={(a,b,c,d):3a+d=0} show that: a) U1 + U2 = R^4; b) U2 + U3 = R^4; c) U1 + U3 = R^4; whish of the sums are direct sum?
 December 1st, 2018, 10:58 AM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,324 Thanks: 1233 can you write down the basis vectors for each of of the U's? If so for each problem use those to find the basis of the sum and use Gaussian elimination to find the resulting basis. If the equality is true you should end up with a 4x4 Identity matrix. U1 spans $R^2$ U2 spans $R^2$ U3 spans $R^3$ So if I understand the term direct sum it should be pretty obvious which pair of these is the only possible candidate for a direct sum. Thanks from Erke Last edited by romsek; December 1st, 2018 at 11:52 AM.

 Tags algebra, linear, subspaces, sum

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post zylo Linear Algebra 5 May 24th, 2016 11:20 AM Alex010 Linear Algebra 1 May 10th, 2016 11:19 AM matqkks Linear Algebra 1 February 7th, 2012 02:39 PM Warpenguin Linear Algebra 1 August 31st, 2011 06:40 AM Babaloo2u Linear Algebra 1 November 10th, 2010 04:33 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top