Question

If the linear transformation TER! - R is defined as T|| :D of T is 24+x;] then the nullity a) 1 b) c) 3 d) o

Answer 1

Option (d) is correct.

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Ang T R² – IRE Tlx, Xit 3 X2 (XJ) - 24,+x, We know that viellity is dimension of Niellspace of T (N(T)). It means Nullity=dem (N(T)). Now by definition N(T) = 263) er?!" :))-1:72 det (2) ENCT) (13)= [:)] = x,+ 3x 12x + x 5) 2,+ 3x, = 0 2x + x = 0 = [1 375x7 107 (In matrix form)

It is of the AX=0 form (Homogeneous system of equations) here A= (1 3 n i 3 (R₂ R₂ - 2 R) O-5 The above matrix is in achlon form, having two non-zero sow, so sank of matrix A is 2. Now im Homogeneous system of equation dimenst dimension of solution space is mnr. 1 ) (here a number of variables 8= sank of matrix A Here dimension & will be m-r-2-2-0 So dimension of Nall space N(T) is zero. So Nullity will be zero. (option (d) is correct.).