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Indicate whether each statement is True or False. Briefly justify your answers. Please answer all of...

Indicate whether each statement is True or False. Briefly justify your answers. Please answer all of questions briefly

(a) In a vector space, if c⊙⃗u =⃗0, then c= 0.

(b) Suppose that A and B are square matrices and that AB is a non-zero diagonal matrix. Then A is non-singular.

(c) The set of all 3 × 3 matrices A with zero trace (T r(A) = 0) is a vector space under the usual matrix operations of addition and scalar multiplication.

(d) Every non-zero vector space Vhas at least two subspaces. Indicate whether each statement is True or False. Briefly justify your answers.

(e) If x⃗1 and x⃗2 are in the null space of a square matrix A, then any linear combination of x⃗1 andx⃗2 is also in the null space of A.

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