Find the Null Space [[a,b,c],[d,e,f],[2g,2h,2i]]=5

Problem

A=[[a,b,c],[d,e,ƒ],[2*g,2*h,2*i]],det(A)=5

Solution

1. Identify the properties of the matrix A based on the given determinant.

2. Recall the definition of the null space, which is the set of all vectors v such that A*v=0

3. Determine the invertibility of the matrix. Since det(A)=5 and 5≠0 the matrix A is non-singular (invertible).

4. Apply the property of invertible matrices. If a matrix A is invertible, the only solution to the homogeneous equation A*v=0 is the trivial solution v=0

5. Conclude that the null space consists only of the zero vector.

Final Answer

Null(A)={0}

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