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Which of the following statements must be true?
(i) If a matrix A has trivial null space, Nul (A) = 0, then the linear transformation x → Ax is one-to-one.
(ii) If A is a 3 x 5 matrix, then the linear transformation x→Ax can not be one-to-one.
(iii) If A is the standard matrix of the linear transformation T that maps from R⁴ to R², then T can not be onto.
(iv) Every linear transformation from Rⁿ to Rᵐ is a matrix transformation.
(v) Let T be a linear transformation that maps from R² to R² that rotates points around the origin by 180° clockwise. T is both one-to-one and onto.
A. (ii), (iv) and (v) only.
B. (i), (iii), and (iv) only.
C. (ii), (iii), and (iv) only.
D. (i), (ii), (iv) and (v) only.
E. (i), (ii), (iii), (iv) and (v).

Sagot :

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