hkus10 Posted March 10, 2011 Share Posted March 10, 2011 Determine whether the given vector A in 2x2 matrix belongs to span{A1, A2, A3}, where A1 = [1 -1 0 3] A2 = [1 1 0 2] A3 = [2 2 -1 1] A = [5 1 -1 9]. Since A1, A2, A3 are not a nx1 matrices, I cannot put this into reduced echelon form? Therefore, what can I do to solve this problem? Thanks Link to comment Share on other sites More sharing options...

timo Posted March 10, 2011 Share Posted March 10, 2011 You write down a condition for A being an element of span{A1,A2,A3} and see if the resulting equations can be satisfied. Link to comment Share on other sites More sharing options...

acidhoony Posted March 16, 2011 Share Posted March 16, 2011 you may got c1A1 + c2A2 + c3A3 = (a b) (c d) which a,b,c,d are arbitary real number maybe~ if you can find c1,2,3for every a,b,c,d then it A1,2,3 is span all 2 by 2 Matrix. but i think it will not span. Because a,b,c,d is fourrr v variable but so we need at least for basis but we have only A1,2,3 ; only three ;;; i don;t know it is dependent or not , but , whatever it is it is too little number of matrix to span every two by two matrix~ Link to comment Share on other sites More sharing options...

the tree Posted March 16, 2011 Share Posted March 16, 2011 (edited) The simplest, crudest approach is to write it as a set of linear equations and look for a solution from there. If [imath]c_1 A_1 + c_2 A_2 + c_2 A_2 = A[/imath], then that implies four equations that can be reduced using good old fashioned elimination. The more mathsy approach would be to summarise the the set described by [imath]\mbox{span}( A_1 , A_2 , A_3 )[/imath] in such a way that it's obvious whether or not [imath]A[/imath] is included. As Acidhoony said, that set is going to be at most 3-dimensional. Edited March 16, 2011 by the tree Link to comment Share on other sites More sharing options...

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