Find the Null Space [[1,0],[0,1]]

Problem

Null Space*[[1,0],[0,1]]

Solution

1. Identify the matrix A and the definition of the null space. The null space consists of all vectors x such that A*x=0

A=[[1,0],[0,1]]

2. Set up the homogeneous system of linear equations A*x=0 using a vector x=[[(x_1)],[(x_2)]]

[[1,0],[0,1]]*[[(x_1)],[(x_2)]]=[[0],[0]]

3. Perform matrix multiplication to create a system of equations.

1*(x_1)+0*(x_2)=0

0*(x_1)+1*(x_2)=0

4. Solve for the variables. The equations directly state that (x_1)=0 and (x_2)=0

x=[[0],[0]]

5. Conclude that since the only solution is the zero vector, the null space contains only the origin. This is expected as the identity matrix is non-singular and has a determinant of 1.

Null(A)={0}

Final Answer

Null Space*[[1,0],[0,1]]={[0],[0]}

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