4.10. Spanning, Linear Independence Basis in R\" 225 Exereise 4.10.22 Here are s
ID: 3115878 • Letter: 4
Question
4.10. Spanning, Linear Independence Basis in R" 225 Exereise 4.10.22 Here are some vectors in R -2-3 Thse vectors can't possibly be linearly independent. Tell why. Next obuima linturly indpendent subset of hese vectors which has the same span as these vectors. In other words. find basis for the span of shese Esercise 410.23 Here are some vectors in R 2-2 -3 These vecters can' possly be linearly independlent. Tell wy. Neat obale a linearly independent saet o hese vectors which has the some span as hese vectors. In other wonds, find a basis for the sppan ef these Exercise 410.24 Mere are some vectors i R Thse vecterws can T possibly be linearly independent. Tell why. Next obtain a linearly independent swbset hese vectors which has the some span as these vectors. In other wonds, Jind a basis for the span of these Esercise 4.10.25 Here are some vectors in R Thse vectews can T possibly be linearly independent Tell why.Next obtoin a linearly independent swbset o nese vectors which has the same span as these vectors. In other wonds, ind a basis for the span ef these Exercise 4.10.26 Here are some vectors in R -1Explanation / Answer
4.10.24. We know that the dimension of R is R4 and that the set of any vectors in R4, having more than 4 vectors is linearly dependent. Here, the given set has 5 vectors in R4. Therefore, this set has to be linearly dependent. Let A be the matrix with the given vectors as columns. Then the RREF of A is
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Apparently, the 3rd and the 4th columns of A are linear combinations of its first 2 columns. The remaining columns (1st, 2nd and 5th) are linearly independent. Thus, the required basis is { (1,2,-2,1)T,(1,3,-3,1)T,(1,3,-2,1)T}.
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