Question

Find a basis for each of the spaces and determine its dimension. The space of all $2 \times 2$ matrices $A$ such that \[ A\left[\begin{array}{ll} 1 & 1 \\ 1 & 1 \end{array}\right]=\left[\begin{array}{ll} 0 & 0 \\ 0 & 0 \end{array}\right] \]

          Find a basis for each of the spaces and determine its dimension.
The space of all $2 \times 2$ matrices $A$ such that
\[
A\left[\begin{array}{ll}
1 & 1 \\
1 & 1
\end{array}\right]=\left[\begin{array}{ll}
0 & 0 \\
0 & 0
\end{array}\right]
\]

Added by Amanda P.

Linear Algebra and Its Applications

David C. Lay, Steven R. Lay, Judi J.… 5th Edition

Instant Answer

Solved by Expert Ben Blakesley

06/06/2022

Step 1

We are given that $A\begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix} = \begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}$. ** Show more…

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Find a basis for each of the spaces and determine its dimension. The space of all $2 \times 2$ matrices $A$ such that \[ A\left[\begin{array}{ll} 1 & 1 \\ 1 & 1 \end{array}\right]=\left[\begin{array}{ll} 0 & 0 \\ 0 & 0 \end{array}\right] \]