GHW3 Data (Excel) (1) - Excel Page Layout Formulas Data Review View Developer Te
ID: 3169568 • Letter: G
Question
GHW3 Data (Excel) (1) - Excel Page Layout Formulas Data Review View Developer Tell me what you want to do General B 1 u .1 HI . 2 . A- Merge & Center-5 . % , Conditional Formato Formatting Table Font Alignment Number Styles 10) 2. Given a collection of vectors W W, W W W, Ws, and a vector b. (Pbm 2) Let w = Span(W) (a) is b eW? Explain. f so, write b as a linear combination of the w (b) Let u= Span( wub) . Is u=w? Explain. (c) How many vectors are in a basis for For ? w1 w5 2.1 -5.2 1.5 4.6 5.4 -3.8 1.9 5.6 2.7 -5.4 3.2 1.6 5.3 0.1 1.3 0.6 3.3 2.3 0.2 5.6 1.7 2.4 1.2 0.8 -2.6 8.6 5.2 4.2 -2.1 2.9Explanation / Answer
2.(a).Let A = [w1,w2,w3,w4,w5,b] =
1
-2.1
1.4
2.7
5.3
3.3
2.3
-5.2
0.2
-5.4
-0.1
-1
-5.3
-1.5
-4.5
3.2
-1.3
-2.9
-1.4
-4.6
-5.2
-1.6
-0.6
0.8
-5.6
-5.4
-5.2
3.4
-3.1
-2.6
1.7
-3.8
-1
4.2
-2.1
8.6
2.4
-1.9
-2.2
-2.6
1.3
4.4
1.2
5.6
2.9
4.9
2.1
4.4
To determine whether b W’ =span{W}, we will reduce A to its RREF , which is
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
-1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
It is now apparent that b W’ =span{W} and b = 2w1+0w2-w3+w4+0w5.
(b). Since b W’ =span{W}, therefore U = span{W U b} = W’.
(c ). It is apparent from the RREF of A that W is a linearly independent set. Hence, there are 5 vectors in a basis for W as also U.
Note: I have usedthe RREF calculator available at www.math.odu.edu/~bogacki/cgi-bin/lat.cgi?c=rref
1
-2.1
1.4
2.7
5.3
3.3
2.3
-5.2
0.2
-5.4
-0.1
-1
-5.3
-1.5
-4.5
3.2
-1.3
-2.9
-1.4
-4.6
-5.2
-1.6
-0.6
0.8
-5.6
-5.4
-5.2
3.4
-3.1
-2.6
1.7
-3.8
-1
4.2
-2.1
8.6
2.4
-1.9
-2.2
-2.6
1.3
4.4
1.2
5.6
2.9
4.9
2.1
4.4
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