Answer:
Dimension of the solution space of the homogeneous system =dimension of kernel=3.
Step-by-step explanation:
Given a matrix has 3 rows and 5 columns .
Dimension of Domain=Number of columns in the matrix=5d
Dimension of the row space =2d
We know that dimension of row space= rank of matrix=2d
Rank-nullity theorem : Rank+nullity= dimension of domain=Number of columns in the matrix.
By using rank-nullity theorem
2+nullity=5
Nullity=5-2
Nullity=3
Dimension of kernel=3d
Dimension of kernel=Dimension of solution space
Dimension of solution space=3d
Hence, the dimension of solution space of the homogeneous system =3d.
