Let $A$ be an invertible matrix of order $n$. What are the kernel, the image, and the rank of the matrix $\begin{bmatrix} A & A \end{bmatrix}$ (of order $n \times 2n$)?
2026-04-09 07:45:07.1775720707
Finding the kernel , the image and the rank of $[A\ A]$ for an invertible $A$
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Hint:
$$\begin{bmatrix} A & A \end{bmatrix} \begin{bmatrix} x \\ x \end{bmatrix} = Ax + Ax = 2Ax.$$