Find the Nullity [[100],[3]]

Problem

nullity*[[100],[3]]

Solution

1. Identify the dimensions of the given matrix A The matrix A=[[100],[3]] is a 2×1 matrix, meaning it has n=1 column.

2. Determine the rank of the matrix. Since the matrix contains at least one non-zero entry, its columns are linearly independent. Thus, rank(A)=1

3. Apply the Rank-Nullity Theorem, which states that for any matrix with n columns, rank(A)+nullity(A)=n

4. Substitute the known values into the theorem: 1+nullity(A)=1

5. Solve for the nullity: nullity(A)=1−1=0

Final Answer

nullity*[[100],[3]]=0

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