Bb Homework sheet 7- M3 x C Chegg Study I Guided Sol X G screenshot on windows X https:// scsu black board.com /webapps/blackboard/execute/content/file?cmd view&content; id 619759 1&course; id 014358 Faculty Information Syllabus M314Work Sheet 7.pdf Lecture Notes INSTRUCTIONS TO CANDIDATE: Show your work Tools Calculators are allowed for addition and subtraction. pts Discussion Board Problem 1 Let W be a subset of R3 defined by My Grades Email Blackboard Help for Students a. Write down two vectors in the set W b. Verify that W is a subspace of R3 and give a geometric interpretation of W. Problem 2 Let W be a subset of R3 defined by ari ERY a. Write down two vectors in the set W b. Verify that W is a subspace of R3 and give a geometric interpretation of W 1 3 1 2 3 Problem 3 Letting A 1 0 1 and A 2 3 8 turn 3 2 17 1 1 0 a. Determine whether the columns of A are linearly independent/dependent b. Determine whether or no 2 and are in the column space of A c. Find the product of the two matrices above. Problem 4 a. Find a basis and dimension for the null space of B b. Find a basis and dimension for the Columnn pace of B in two ways 1 2 4 -1 1 HW from TEXT Section 3.2 Problems 1-17odd, 23 Section 3.3 Problems 1-25 odd, 34,35 Section 3.4 Problems 1-15 odd N 9:16 AM 4/25/2016
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(a) Two vectors are (1,3,2) and (0,4,4)
(b) Now,we prove that W is a subspace of R3
(i) 0=0-0, so (0,0,0) belongs to W
(ii) Let u=(a,b,c),v=(d,e,f) be any two elements of W, then
a=b-c and d=e-f
So, a+d= b+e-(c+f)
Thus, u+v= (a+d, b+e, c+f) belongs to W
(iii) Let k be any scalar and let u=(a,b,c) belongs to W
Then, a=b-c
i.e. ka=kb-kc
So, (ka,kb,kc)=k(a,b,c) belongs to W
Thus, W is a subspace of R3
2.
(a) Two vectors are (1,4,1) and (2,8,2)
(b) Now,we prove that W is a subspace of R3
(i) 0=0+3(0), so (0,0,0) belongs to W
(ii) Let u=(a,b,c),v=(d,e,f) be any two elements of W, then
b=a+3c and e=d+3f
So, b+e= a+d+3(c+f)
Thus, u+v= (a+d, b+e, c+f) belongs to W
(iii) Let k be any scalar and let u=(a,b,c) belongs to W
Then, b=a+3c
i.e. kb=ka+3kc
So, (ka,kb,kc)=k(a,b,c) belongs to W
Thus, W is a subspace of R3
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