Question

(5) Which of the following sets is a subspace of $M_{3 \times 3}$ (the vector space of 3 × 3 matrices)? (A) S = \{$A \in M_{3 \times 3}$ : NulA contains $e_1$\}. (B) S = \{$A \in M_{3 \times 3}$ : det $A = 0$\}. (C) S = \{$A \in M_{3 \times 3}$ : $A^T A = I_3$\}. (D) S = \{$A \in M_{3 \times 3}$ : A is diagonalizable\}. (E) None of the above.

          (5) Which of the following sets is a subspace of $M_{3 \times 3}$ (the vector space of 3 × 3 matrices)?
(A) S = \{$A \in M_{3 \times 3}$ : NulA contains $e_1$\}.
(B) S = \{$A \in M_{3 \times 3}$ : det $A = 0$\}.
(C) S = \{$A \in M_{3 \times 3}$ : $A^T A = I_3$\}.
(D) S = \{$A \in M_{3 \times 3}$ : A is diagonalizable\}.
(E) None of the above.

$(5) Which of the following sets is a subspace of M3 × 3 (the vector space of 3 × 3 matrices)? (A) S = {A ∈ M3 × 3 : NulA contains e1}. (B) S = {A ∈ M3 × 3 : det A = 0}. (C) S = {A ∈ M3 × 3 : A^T A = I3}. (D) S = {A ∈ M3 × 3 : A is diagonalizable}. (E) None of the above.$

Added by Francisco A.

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