Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Linear Algebra Linear Dependence, Basis & Dimension
A. Suppose U and W are finite - dimensional subspace of a vector space V, then dim (U + W) = dim U + dim W - dim (U ∩ W) .
B. let V = R3.W = {(a, b, c : a ≥ 0)}, then W is a subspace of V
C. If u = (1, 2), v = (-3, -5), then u and v are linearly independent
D. (1, 1, 1) and (1, 0, 1) form a basis of R3
choose the most appropriate answer from the options given below
1
A, C Only
2
A, D Only
3
B, C Only
4
B, D Only