Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Analysis Vector Spaces
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?
1
Both P and Q are true
2
P is true but Q is false
3
P is false but Q is true
4
Both P and Q are false