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Introduction to Linear Algebra

Exercise 3.4.24

Answers

(a): False $A = [\begin{matrix} 1 & 1 \end{matrix}]$ has dependent columns, independent row
(b): False Column space $≠$ row space for $A = [\begin{matrix} 0 & 1 \\ 0 & 0 \end{matrix}]$
(c): True: Both dimensions $= 2$ if $A$ is invertible, dimensions $= 0$ if $A = 0$ , otherwise dimensions $= 1$
(d): False, columns may be dependent, in that case not a basis for $C (A)$ .

mathchakra

2022-01-23 15:52

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