# Basis and basis matrices

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3. Let B1 = {v1,v2,v3} be a basis of vector space V and B2 = {w1,w2,w3} where

w1=v2+v3; w2=v1+v3; w3= v1+v2

Verify that B2 is also a basis of V and find the change of basis matrices from B1 to B2 and from B2 to B1. Express the vector a(v1) +b(v2) + c(v3) as a linear combination of w1,w2,w3

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This shows how to verify a basis and find change of basis matrices.

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let B1 = {v1,v2,v3} be a basis of vector space V and B2 = {w1,w2,w3} where

w1=v2+v3; w2=v1+v3; w3= v1+v2

verify that B2 is also a basis of V and find the change of basis matrices from B1 to B2 and from B2 to B1. express the vector a(v1) ...

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- BSc , Wuhan Univ. China
- MA, Shandong Univ.

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- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
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