For each linear transformation below, state a basis for Ker(T), the Nullity of the transformation, and the Rank of the transformation. If you do not need a vector, then place zeros for all entries of that vector (for example, if you only need 2 vectors for the basis, then fill in the first two vectors and make all subsequent vectors have 0 for all boxes). la +16+lc 1) Let T 2a+3b+3c] -la+(-2)b+ (-2)c 3a+3b+3c i) A basis for Ker(T) would be: ii) The Nullity of T is: iii) The Rank of T is: [la+16+2c+2d 2) Let T(a + bx + cx² + dx³) = la+2b+1c+1d 2a+3b+4c+ 2d -la + (-3)b+ (-1)c+2d] i) A basis for Ker(T) would be: ii) The Nullity of T is: iii) The Rank of T is: T 3) Let T a b de C 3 la+(-1)6+1c+ (-1)d + 2e+4f 2a+(-1)b+4c+4d + 6e + 12f Oa+(-1)b+(-1)c+ (-4)d+ (-1)e + (-2) f 6a+(-3)b+11c + 10d + 18e + 34f i) A basis for Ker(T) would be: 1888 1889 1888 1888-1888)

Please check the right statement(s) ○ " ▼. Ď is a scalar 1) V x H is a scalar 1. Dis a vector OMVxH is a vector On VV is a vector Ovi) VV is a scalar

Consider the scalar systern x(t) = tx(t) Compute the state matrix Ølt₂t.). transition

Determine si los campos vectoriales mostradosson conservativos o no lo son, y si lo son encuentra una funcion potencial F=(10x+3y)i+(3x+20y)j

I help to see if my answer in performing the vector operation is correct The answer I got was: a) 500 ∠ 110o b) 1600 ∠ -50o c) 3 + j0