Answer:
Given:
Weight of solid in air, 
Weight of solid in water, 
Weight of solid in liquid, 
Solution:
Calculation of:
1. Relative density of solid, 
2. Relative density of liquid, 
3. Density of liquid in S.I units:
Also, we know:
where
= density of liquid
= density of water
Now, from the above formula:
Answer:
The dimension of the nullspace of T = 4
Explanation:
The rank/dimension theorem is explains that:
Suppose V and W are vector spaces over F, and T:V → W is linear. If V is finite dimensional, then
nullity(T) + rank(T) = dim(V).
rank(T) = dimension of T = dim(T) = dim(W) = 7
nullity(T) = dimension of the nullspace of T = dim(T) = ?
dim(V) = 11
nullity(T) = dim(V) - dim(T) = 11 - 7
nullity(T) = 4.
