Show that if s1 and s2 are subsets of a vector space v such that s1 c s2 then span(s1) c span(s2). in particular, if s1 c s2 then span(s1)

See proof below

Step-by-step explanation:

Assume that V is a vector space over the field F (take F=R,C if you prefer).

Let . Then, we can write x as a linear combination of elements of s1, that is, there exist and such that . Now, then for all we have that . In particular, taking with we have that . Then, x is a linear combination of vectors in S2, therefore . We conclude that .

If, additionally   then reversing the roles of S1 and S2 in the previous proof, . Then , therefore .

13

step-by-step explanation:

169-1=168

168-3=165

165-5=160

160-7=153

153-9=144

144-11=133

133-13=120

120-15=105

105-17=88

88-19=69

69-21=48

48-23=25

25-25=0

since it took 13times to completely subtract it hence its square root is 13

step-by-step explanation:

if you want to solve percent error follow these steps.

1. subtract the accepted value from the experimental value.

2. take the absolute value of step 1.

3. divide that answer by the accepted value.

4. multiply that answer by 100 and add the % symbol to express the answer as a percentage.

if you want to solve percent of change just do this.

1. work out the difference (increase) between the two numbers you are comparing.

2. divide the increase by the original number and multiply the answer by 100. if your answer is a negative number then this is a percentage decrease.

hope this : )