Find the Nullity [[17,22,4],[2,9,11],[4,6,13]]

Problem

nullity*[[17,22,4],[2,9,11],[4,6,13]]

Solution

1. Set up the matrix A and the equation A*x=0 to find the dimension of the null space.

A=[[17,22,4],[2,9,11],[4,6,13]]

2. Calculate the determinant of the matrix to determine if it is invertible.

det(A)=17*(9⋅13−11⋅6)−22*(2⋅13−11⋅4)+4*(2⋅6−9⋅4)

3. Simplify the arithmetic for the determinant.

det(A)=17*(117−66)−22*(26−44)+4*(12−36)

det(A)=17*(51)−22*(−18)+4*(−24)

det(A)=867+396−96

det(A)=1167

4. Apply the Rank-Nullity Theorem which states that for an n×n matrix, rank(A)+nullity(A)=n

det(A)≠0⇒rank(A)=3

5. Solve for the nullity using n=3

nullity(A)=3−3

nullity(A)=0

Final Answer

nullity*[[17,22,4],[2,9,11],[4,6,13]]=0

Want more problems? Check here!