1.1.4 From v = (2,1) and w = (1,2) find the components of 3v + w and cv + dw

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1.1.4-Finding Components of 3v + w and cv + dw | Linear Algebra (Gilbert Strang, 5th Ed.) 1.1.4-Finding Components of 3v + w and cv + dw | Linear Algebra (Gilbert Strang, 5th Ed.)
1.1.17 Locate 1/3v + 1/3w and 2/3v + 2/3w. The combinations cv + dw fill out what line? 1.1.17 Locate 1/3v + 1/3w and 2/3v + 2/3w. The combinations cv + dw fill out what line?
1.1.28 Find vectors v and w so that v + w = (4,5,6) and v - w = (2,5,8). 1.1.28 Find vectors v and w so that v + w = (4,5,6) and v - w = (2,5,8).
1.1.16 Mark the point -v + 2w and any other combination cv + dw with c + d = 1. 1.1.16 Mark the point -v + 2w and any other combination cv + dw with c + d = 1.
1.1.20 Locate 1/3u + 1/3v + 1/3w and 1/2u + 1/2w in Figure 1.5b. 1.1.20 Locate 1/3u + 1/3v + 1/3w and 1/2u + 1/2w in Figure 1.5b.
1.1.15 Figure 1.5a shows 1/2v + 1/2w. Mark the points 3/4v + 1/4w and 1/4v + 1/4w and v + w. 1.1.15 Figure 1.5a shows 1/2v + 1/2w. Mark the points 3/4v + 1/4w and 1/4v + 1/4w and v + w.
1.1.5 Compute u + v + w and 2u + 2v + w. How do you know u, v, w lie in a plane? 1.1.5 Compute u + v + w and 2u + 2v + w. How do you know u, v, w lie in a plane?
1.1.7 In the x y plane mark all nine of these linear combinations: c(2,1) + d(0,1) with c,d = 0,1,2 1.1.7 In the x y plane mark all nine of these linear combinations: c(2,1) + d(0,1) with c,d = 0,1,2