22 The linear transformation T y T is onetoone 23 The linear

(22) The linear transformation T y T is one-to-one (23) The linear transformation in question 22 is onto. (24) If T is the linear transformation in question 22, then T12 -T 1. (25) 1 is an eigenvalue of the linear transformation in question 22 (26) dim(E1) for the linear transformation in question 22.

Solution

22. The statement is True.

23. The statement is True.

24. The statement is True as T²(x,y,z)^T = (y,z,x)^T = T^-1(x,y,z)^T

25. The statement is True.

26. The statement is True. E₁ = span{(1,1,1)^T}.

42. The statement is True.

43. The statement is False.

Note: Before saying True or False, calculations are involved.