Question

(a) Let F be the field of complex numbers and let T be the function from P3 into F3 defined by
T(x1 X2 X3) = (x1 - x2 + 2x3,2x1 + x2. - Xı - 2 x2 + 2x3)
1. Verify that T is a linear transformation.
If (a,b,c) is a vector in F3, what are the conditions on a, b and c that the vector be
in the range of 7? What is the rank of T?
What are the conditions on a,b and c that the vector (a,b,c) be in the null space of
T? What is the nullity of T?
(b) Let T be the linear operator on R defined by
T(X1 X2 X3) = (3x, *; - *2.2x, + x2 + x3)
Is T invertible? If so, find a rule for T-1 like the one which defines T.​

Answer 1

Answer:

If one angle of a parallelogram is 36° less than twice its adjacent angle, then find the smallest

angle of parallelogram.