This is where matrix multiplication comes in: if we think of c1 and c2 as the columns of

Chapter 12, Problem 12.5.16

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This is where matrix multiplication comes in: if we think of c1 and c2 as the columns of a matrix C, we see that 9 8 = 1 2 c1 3 1 c2 3 2 is the same as 9 8 = 3 1 2 c1 +2 3 1 c2 . In general, if v = Cu , then the coordinates of u tell us how to combine the columns of C in order to get v . (a) Let v = 3 r1 + 5 r2 where r1 = (3, 2) and r2 = (0, 1). Find v , u , and R such that v = Ru . (b) Let q = Sp = 3 4 2 3 3 2 . Show that q can be written as a combination of s1 = (3, 2) and s2 = (4, 3), the two columns of S. 17. Let v = (2, 5), c1 = (3, 2 This is where matrix multiplication comes in: if we think of c1 and c2 as the columns of a matrix C, we see that 9 8 = 1 2 c1 3 1 c2 3 2 is the same as 9 8 = 3 1 2 c1 +2 3 1 c2 . In general, if v = Cu , then the coordinates of u tell us how to combine the columns of C in order to get v . (a) Let v = 3 r1 + 5 r2 where r1 = (3, 2) and r2 = (0, 1). Find v , u , and R such that v = Ru . (b) Let q = Sp = 3 4 2 (b) Let q = Sp = 3 4 2 3 3 2 . Show that q can be written as a combination of s1 = (3, 2) and s2 = (4, 3), the two columns of S. 17.

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