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Question

The linear combination of ¯a=[12]and¯b=[03] which gives the vector [22] will be ___¯a +__ ¯b. (If any of the blanks is a fraction, enter the value to the nearest hundredth place).

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Solution

A linear combination of ¯a and ¯b can be written as c1¯a+c2¯b
So c1¯a+c2¯b=[22]
or c1[12]
+c2[03] =[22]
This gives
(c1×1)+(c2×0)=2....(1)
(c1×2)+(c2×3)=2....(2)
Multiply equation (1) by -2
2c1+0=4
2c1+3c2=2––––––––––––– Now add these equations.
3c2=2
c2=23=1.66
Also from equation (1)
c1=2
So
c1=2
c2=1.66
Linear combination will be
2¯a1.66¯b=[12]

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