Valid convolution output

Tutor me on https://mlprep.iwase.dev/item/ml-screen-convolution-foundation-operation/. This is a screening item. If window.mlPrepAgent is available, read attempts for item ml-screen-convolution-foundation-operation before tutoring. Inspect my attempt, keep the item ID, and do not reveal the full answer first. After a real attempt, append its record with recorded_by agent, include agent_session_id when available, and read it back.

Problem

Using the cross-correlation convention common in neural-network libraries, apply

K=\begin{bmatrix}1&0\\0&-1\end{bmatrix}

with stride $1$ and no padding to

X=\begin{bmatrix}1&2&3\\4&5&6\\7&8&9\end{bmatrix}.

Give the output matrix.

Reveal answer or reference solution

Each output is the top-left patch value minus the bottom-right patch value. The output is

\begin{bmatrix}1-5&2-6\\4-8&5-9\end{bmatrix}=\begin{bmatrix}-4&-4\\-4&-4\end{bmatrix}.

The kernel is not flipped because the prompt specifies cross-correlation.

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Valid convolution output

Problem

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