Mathematics II20755 marksNumerical: null space and column space dimensionNull spaces, Column spaces, and Linear transformations
Find the dimension of the null space and column space of A = beginbmatrix -3 & 6 & -1 & 1 & -7 1 & -2 & 2 & 3 & -1 2 & -4 & 5 & 8 & -4 endbmatrix
Find the dimension of the null space and column space of $A = \begin{bmatrix} -3 & 6 & -1 & 1 & -7 \ 1 & -2 & 2 & 3 & -1 \ 2 & -4 & 5 & 8 & -4 \end{bmatrix}$ [5]
$$A = \begin{bmatrix} -3 & 6 & -1 & 1 & -7 \ 1 & -2 & 2 & 3 & -1 \ 2 & -4 & 5 & 8 & -4 \end{bmatrix}, \quad 3 \times 5 \text{ matrix}$$ Number of columns $n = 5$. Swap $R1 \leftrightarrow R2$: $$\begin{bmatrix} 1 & -2 & 2 & 3 & -1 \ -3 & 6 & -1 & 1 & -7 \ 2 & -4 & 5 & 8 & -4 \end{bmatrix}$$