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explain this example how k=3 and 4

EXAMPLE 5 Let $A=⎣⎡ 2−23 4−57 −27−8 136 ⎦⎤ $ a. If the column space of $A$ is a subspace of $R_{k}$, what is $k$ ? b. If the null space of $A$ is a subspace of $R_{k}$, what is $k$ ? SOLUTION a. The columns of $A$ each have three entries, so $ColA$ is a subspace of $R_{k}$, where $k=3$ b. A vector $x$ such that $Ax$ is defined must have four entries, so Nul $A$ is a subspace of $R_{k}$, where $k=4$.

given matrix

we first find the column space of A

By the definition

Column space of A=span of the columns of A

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