Find the Null Space x=[[5],[8],[3]]ax=0

Problem

A=[[5],[8],[3]],A*x=0

Solution

1. Identify the matrix A and the equation for the null space. The matrix A is a 3×1 matrix, and we are looking for all vectors x=[(x_1)] such that A*x=0

2. Set up the system of linear equations. Multiplying the 3×1 matrix A by a 1×1 vector (x_1) gives:

5*(x_1)=0

8*(x_1)=0

3*(x_1)=0

3. Solve for the variable (x_1) From any of the three equations, it is clear that the only solution is:

(x_1)=0

4. Determine the null space. Since the only solution to the homogeneous equation is the zero vector, the null space contains only the zero vector.

Final Answer

Null(A)={[(0)]}

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