Question

Consider the following statements.
P : If a system of linear equations Ax = b has a unique solution, where A is an m × n matrix and b is an m × 1 matrix, then m = n.
Q : For a subspace W of a nonzero vector space V, whenever u ∈ V ∖ W and v ∈ V ∖ W, then u + v ∈ V ∖ W.
Which one of the following holds ?

• A. Both P and Q are true
• B. P is true but Q is false
• C. P is false but Q is true
• D. Both P and Q are false

Answer 1

Answer: (D)

Both P and Q are false

Answer 2

The correct option is (D) : Both P and Q are false.