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Linear Systemshard
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Solve the homogeneous system and express the solution as a linear combination of basis vectors for the null space: [12030012][x1x2x3x4]=[00]\begin{bmatrix} 1 & 2 & 0 & 3 \\ 0 & 0 & 1 & 2 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \\ x_4 \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix}[10​20​01​32​]​x1​x2​x3​x4​​​=[00​]

What is the dimension of the null space?