Find the Nullity [[1],[-2]]

Problem

Nullity*[[1],[−2]]

Solution

1. Identify the dimensions of the matrix A The given matrix A=[[1],[−2]] 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 rank is the number of linearly independent columns.

rank(A)=1

3. Apply the Rank-Nullity Theorem. The theorem states that for any m×n matrix, the sum of the rank and the nullity equals the number of columns n

rank(A)+nullity(A)=n

4. Substitute the known values into the formula to solve for the nullity.

1+nullity(A)=1

5. Calculate the final value.

nullity(A)=0

Final Answer

Nullity*[[1],[−2]]=0

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