The dimension of the row space of a 3 x 5 matrix A is 2 d. What is the dimension of the solution space of the homogeneous system Ax = 0?

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=5dDimension of the row space =2dWe know that dimension of row space= rank of matrix=2dRank-nullity theorem : Rank+nullity= dimension of domain=Number of columns in the matrix.By using rank-nullity theorem 2+nullity=5Nullity=5-2Nullity=3Dimension of kernel=3dDimension of kernel=Dimension of  solution spaceDimension of solution space=3dHence, the dimension of solution space of the homogeneous system =3d.