Question

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QUESTION 3 6 points Find the value(s) of a € R such that dim(span(A)) = 2 where A = {1+ 2x² + x4,2+x+4x2 +r? +5x*, 1+x+2x² + x + ax"} 0 a=3 0 0 R

Answer 1

Solertion :- Given dim( Spar(A)) = 2 As 1+2x2+24, 2+x+uX?+23+5x4, 1+X+2x2433, تن Soo to know the dimension of Al we need to convert it to reduced row echelon form of Augmentend matrix, and Dimension is the number of non-zero rows in reduced row echelon form, ri 0 2017 A= 12 a 15 L li21a reduced rool To convert it to R2 R2-2R1 Echelon Ato 2017 R3 > R3-R1. R3= R3-R2 TTO 2 0 1 7 Now lo o o it is in o d-4 the reduced row Echelon Form. Scanned with CamScanner

Now, to get din Spanca)) = 62 We should have only a non-zero rows, So third sow should be zero, then din (span A)=2 So d-u=0 → 1224 gold s , cs Scanned with CamScanner